Webkit支持边界渐变，现在也接受Mozilla格式的渐变。

Firefox以两种方式支持渐变:

使用border-image和border-image-source 使用border-right-colors(右/左/上/下)

IE9不支持。

试试这段代码

.gradientBoxesWithOuterShadows { 
height: 200px;
width: 400px; 
padding: 20px;
background-color: white; 

/* outer shadows  (note the rgba is red, green, blue, alpha) */
-webkit-box-shadow: 0px 0px 12px rgba(0, 0, 0, 0.4); 
-moz-box-shadow: 0px 1px 6px rgba(23, 69, 88, .5);

/* rounded corners */
-webkit-border-radius: 12px;
-moz-border-radius: 7px; 
border-radius: 7px;

/* gradients */
background: -webkit-gradient(linear, left top, left bottom, 
color-stop(0%, white), color-stop(15%, white), color-stop(100%, #D7E9F5)); 
background: -moz-linear-gradient(top, white 0%, white 55%, #D5E4F3 130%); 
}

或者可以参考这个小提琴:http://jsfiddle.net/necolas/vqnk9/

渐变边框来自Css-Tricks: http://css-tricks.com/examples/GradientBorder/

.multbg-top-to-bottom {
  border-top: 3px solid black;
  background-image: -webkit-gradient(linear, 0 0, 0 100%, from(#000), to(transparent));
  background-image: -webkit-linear-gradient(#000, transparent);
  background-image:
      -moz-linear-gradient(#000, transparent),
      -moz-linear-gradient(#000, transparent);
  background-image:
      -o-linear-gradient(#000, transparent),
      -o-linear-gradient(#000, transparent);
  background-image: 
      linear-gradient(#000, transparent),
      linear-gradient(#000, transparent);
  -moz-background-size: 3px 100%;
  background-size: 3px 100%;
  background-position: 0 0, 100% 0;
  background-repeat: no-repeat; 
}

这是一个带有透明背景的渐变边界，使用边界半径

.gradient-border {
  border-radius: 999px;
  padding: 10px 3rem;
  display: inline-block;
  position: relative;
  background: transparent;
  border: none;
}

.gradient-border::before {
  content: "";
  position: absolute;
  inset: 0;
  padding: 2px;
  border-radius: 9999px;
  background: linear-gradient(87.36deg, blue 6.42%, red 84.24%),
linear-gradient(0deg, #FFFFFF, #FFFFFF);
  -webkit-mask: 
     linear-gradient(#fff 0 0) content-box, 
     linear-gradient(#fff 0 0);
          mask: 
     linear-gradient(#fff 0 0) content-box, 
     linear-gradient(#fff 0 0);
  -webkit-mask-composite: xor;
          mask-composite: exclude;
}

现场演示:https://jsfiddle.net/jbernier/0eypxc74/1/

最直接的方法是使用border-image属性。你可以使用任何你想要的线性渐变或重复渐变。对于线性梯度，边界图像切片属性需要为1。

.gradient-border {
    border-style: solid;
    border-width: 2px;
    border-image: linear-gradient(45deg, red, blue) 1;
}

参考文献 MDN - https://developer.mozilla.org/en-US/docs/Web/CSS/border-image-slice 数字海洋- https://www.digitalocean.com/community/tutorials/css-gradient-borders-pure-css

我同意szajmon的观点。他和昆汀回答的唯一问题是跨浏览器兼容性。

HTML:

<div class="g">
    <div>bla</div>
</div>

CSS:

.g {
background-image: -webkit-linear-gradient(300deg, white, black, white); /* webkit browsers (Chrome & Safari) */
background-image: -moz-linear-gradient(300deg, white, black, white); /* Mozilla browsers (Firefox) */
filter: progid:DXImageTransform.Microsoft.gradient(startColorstr='#ffffff', endColorstr='#000000', gradientType='1'); /* Internet Explorer */
background-image: -o-linear-gradient(300deg,rgb(255,255,255),rgb(0,0,0) 50%,rgb(255,255,255) 100%); /* Opera */
}

.g > div { background: #fff; }