可以通过加载一个小的 WebP 图片，来判断浏览器是否支持 WebP。

// check_webp_feature:
// 'feature' can be one of 'lossy', 'lossless', 'alpha' or 'animation'.
// 'callback(feature, result)' will be passed back the detection result (in an asynchronous way!)
function check_webp_feature(feature, callback) {
    var kTestImages = {
        lossy: "UklGRiIAAABXRUJQVlA4IBYAAAAwAQCdASoBAAEADsD+JaQAA3AAAAAA",
        lossless: "UklGRhoAAABXRUJQVlA4TA0AAAAvAAAAEAcQERGIiP4HAA==",
        alpha: "UklGRkoAAABXRUJQVlA4WAoAAAAQAAAAAAAAAAAAQUxQSAwAAAARBxAR/Q9ERP8DAABWUDggGAAAABQBAJ0BKgEAAQAAAP4AAA3AAP7mtQAAAA=="
        animation: "UklGRlIAAABXRUJQVlA4WAoAAAASAAAAAAAAAAAAQU5JTQYAAAD/////AABBTk1GJgAAAAAAAAAAAAAAAAAAAGQAAABWUDhMDQAAAC8AAAAQBxAREYiI/gcA"
    };
    var img = new Image();
    img.onload = function () {
        var result = (img.width > 0) && (img.height > 0);
        callback(feature, result);
    };
    img.onerror = function () {
        callback(feature, false);
    };
    img.src = "data:image/webp;base64," + kTestImages[feature];
}

来源: https://developers.google.com/speed/webp/faq#how_can_i_detect_browser_support_using_javascript