更新:此解决方案于2018年12月停止工作。

我也在找同样的事情，看起来这里的大多数答案都过时了，因为Vimeo API v2已弃用。

我的PHP 2¢:

$vidID     = 12345 // Vimeo Video ID
$tnLink = json_decode(file_get_contents('https://vimeo.com/api/oembed.json?url=https%3A//vimeo.com/' . $vidID))->thumbnail_url;

通过上面的链接，你将得到Vimeo默认缩略图的链接。

如果你想使用不同大小的图像，你可以添加如下内容:

$tnLink = substr($tnLink, strrpos($tnLink, '/') + 1);
$tnLink = substr($tnLink, 0, strrpos($tnLink, '_')); // You now have the thumbnail ID, which is different from Video ID

// And you can use it with link to one of the sizes of crunched by Vimeo thumbnail image, for example:
$tnLink = 'https://i.vimeocdn.com/filter/overlay?src0=https%3A%2F%2Fi.vimeocdn.com%2Fvideo%2F' . $tnLink    . '_1280x720.jpg&src1=https%3A%2F%2Ff.vimeocdn.com%2Fimages_v6%2Fshare%2Fplay_icon_overlay.png';

您应该解析Vimeo API的响应。没有办法用URL调用(如dailymotion或youtube)。

下面是我的PHP解决方案:

/**
 * Gets a vimeo thumbnail url
 * @param mixed $id A vimeo id (ie. 1185346)
 * @return thumbnail's url
*/
function getVimeoThumb($id) {
    $data = file_get_contents("http://vimeo.com/api/v2/video/$id.json");
    $data = json_decode($data);
    return $data[0]->thumbnail_medium;
}

api/v2似乎已经死了。 为了使用新的API，您需要注册应用程序，base64将client_id和client_secret编码为授权标头。

$.ajax({
    type:'GET',
    url: 'https://api.vimeo.com/videos/' + video_id,
    dataType: 'json',
    headers: {
        'Authorization': 'Basic ' + window.btoa(client_id + ":" + client_secret);
    },
    success: function(data) {
        var thumbnail_src = data.pictures.sizes[2].link;
        $('#thumbImg').attr('src', thumbnail_src);
    }
});

为了安全起见，您可以返回已经从服务器编码的client_id和client_secret。

function getVimeoInfo($link)
 {
    if (preg_match('~^http://(?:www\.)?vimeo\.com/(?:clip:)?(\d+)~', $link, $match)) 
    {
        $id = $match[1];
    }
    else
    {
        $id = substr($link,10,strlen($link));
    }

    if (!function_exists('curl_init')) die('CURL is not installed!');
    $ch = curl_init();
    curl_setopt($ch, CURLOPT_URL, "http://vimeo.com/api/v2/video/$id.php");
    curl_setopt($ch, CURLOPT_HEADER, 0);
    curl_setopt($ch, CURLOPT_RETURNTRANSFER, true);
    curl_setopt($ch, CURLOPT_TIMEOUT, 10);
    $output = unserialize(curl_exec($ch));
    $output = $output[0];
    curl_close($ch);
    return $output;
}`

//在下面的函数传递缩略图url。

function save_image_local($thumbnail_url)
    {

         //for save image at local server
         $filename = time().'_hbk.jpg';
         $fullpath = '../../app/webroot/img/videos/image/'.$filename;

         file_put_contents ($fullpath,file_get_contents($thumbnail_url));

        return $filename;
    }

function parseVideo(url) {
    // - Supported YouTube URL formats:
    //   - http://www.youtube.com/watch?v=My2FRPA3Gf8
    //   - http://youtu.be/My2FRPA3Gf8
    //   - https://youtube.googleapis.com/v/My2FRPA3Gf8
    // - Supported Vimeo URL formats:
    //   - http://vimeo.com/25451551
    //   - http://player.vimeo.com/video/25451551
    // - Also supports relative URLs:
    //   - //player.vimeo.com/video/25451551

    url.match(/(http:|https:|)\/\/(player.|www.)?(vimeo\.com|youtu(be\.com|\.be|be\.googleapis\.com))\/(video\/|embed\/|watch\?v=|v\/)?([A-Za-z0-9._%-]*)(\&\S+)?/);

    if (RegExp.$3.indexOf('youtu') > -1) {
        var type = 'youtube';
    } else if (RegExp.$3.indexOf('vimeo') > -1) {
        var type = 'vimeo';
    }

    return {
        type: type,
        id: RegExp.$6
    };
}

function getVideoThumbnail(url, cb) {
    var videoObj = parseVideo(url);
    if (videoObj.type == 'youtube') {
        cb('//img.youtube.com/vi/' + videoObj.id + '/maxresdefault.jpg');
    } else if (videoObj.type == 'vimeo') {
        $.get('http://vimeo.com/api/v2/video/' + videoObj.id + '.json', function(data) {
            cb(data[0].thumbnail_large);
        });
    }
}

2020的解决方案:

我写了一个使用Vimeo Oembed API的PHP函数。

/**
 * Get Vimeo.com video thumbnail URL
 *
 * Set the referer parameter if your video is domain restricted.
 * 
 * @param  int    $videoid   Video id
 * @param  URL    $referer   Your website domain
 * @return bool/string       Thumbnail URL or false if can't access the video
 */
function get_vimeo_thumbnail_url( $videoid, $referer=null ){

    // if referer set, create context
    $ctx = null;
    if( isset($referer) ){
        $ctxa = array(
            'http' => array(
                'header' => array("Referer: $referer\r\n"),
                'request_fulluri' => true,
            ),
        );
        $ctx = stream_context_create($ctxa);
    }

    $resp = @file_get_contents("https://vimeo.com/api/oembed.json?url=https://vimeo.com/$videoid", False, $ctx);
    $resp = json_decode($resp, true);

return $resp["thumbnail_url"]??false;
}

用法:

echo get_vimeo_thumbnail_url("1084537");