只需要在参数后面加 "" 就可以传递数组了

function sendArray() {
    var strArray = ["A","B","C","D"];
    var numArray = [1,2,3,4];
    $.ajax({
        url:"sendArray",
        type:"post",
        data:{
            strArray:strArray+"",
            numArray:numArray+""
        },
        dataType:"json",
        success:function (suc) {
            console.log(suc);
        },
        error:function (err) {
            console.log(err);
        }
    });
}
sendArray();

或者开启Ajax防止深度序列化traditional: true

function sendArray() {
    var strArray = ["A","B","C","D"];
    var numArray = [1,2,3,4];
    $.ajax({
        url:"sendArray",
        type:"post",
        data:{
            strArray:strArray,
            numArray:numArray
        },
        traditional: true,//防止深度序列化
        dataType:"json",
        success:function (suc) {
            console.log(suc);
        },
        error:function (err) {
            console.log(err);
        }
    });
}
sendArray();

后台接收

    @RequestMapping("/sendArray")
    @ResponseBody
    public String sendArray(String[] strArray, Integer[] numArray) {
        System.out.println("strArray:"+strArray[0]+","+strArray[1]+","+strArray[2]);
        System.out.println("numArray:"+numArray[0]+","+numArray[1]+","+numArray[2]);
        return "成功";
    }