根据canisue（​​http://caniuse.com/#search=border-radius），border-radius兼容性如下图所示：​​​border-radius IE8兼容处理_css
测试代码：

<!DOCTYPE html>
<html>

    <head>
        <meta charset="UTF-8">
        <meta http-equiv="X-UA-Compatible" content="IE=edge,chrome=1">
        <title></title>
        <style type="text/css">
            * {
                margin: 0;
                padding: 0;
            }
            
            #header {
                width: 400px;
                height: 400px;
                margin: 10px;
                border-radius: 10px;
                border: 1px solid red;
            }
        </style>
    </head>

    <body>
        <div id="header">
        </div>
    </body>

</html>

IE8浏览器效果：
border-radius IE8兼容处理_css_02
border-radius在IE8浏览器兼容方案：

<!DOCTYPE html>
<html>

    <head>
        <meta charset="UTF-8">
        <meta http-equiv="X-UA-Compatible" content="IE=edge,chrome=1">
        <title></title>
        <style type="text/css">
            * {
                margin: 0;
                padding: 0;
            }
            
            #header {
                width: 400px;
                height: 400px;
                margin: 10px;
                border-radius: 10px;
                border: 1px solid red;
                /*关键属性设置 需要把路径设置好*/
                behavior: url(PIE.htc);
            }
        </style>
    </head>

    <body>
        <div id="header">
        </div>
    </body>

</html>

border-radius IE8兼容处理_html_03

PIE.HTC下载地址：​​http://css3pie.com/​​​border-radius IE8兼容处理_html_04