// ==UserScript==
// @name        name
// @author      author
// @description description
// @namespace   http://tampermonkey.net/
// @license     GPL version 3
// @encoding    utf-8
// @include     https://www.baidu.com/*
// @grant        GM_xmlhttpRequest
// @grant        GM_download
// @run-at      document-end
// @version     1.0.0
// ==/UserScript==

GM_xmlhttpRequest({
    method: "GET",
    url: "http://api.kanzhihu.com/getpostanswers/20150925/archive",
    onload: function(res) {
        if (res.status == 200) {
            var text = res.responseText;
            var json = JSON.parse(text);
            console.log(json);
        }
    }
});

这里重要的是要引用// @grant GM_xmlhttpRequest// @grant GM_download, 然后就可以用GM_xmlhttpRequest函数来执行跨域请求了...