feel like 后面怎么可以加to do呢？

看看区别吧:

feel like doing sth 已做过某事，表明喜欢的感觉
feel like to do sth 还没去做的事情，乐意去做。

feel like doing=want to do
feel like
下面是我网上找的关于feel like的用法.
一、feel like＋名词，意为“觉得好像……”。

It feels like rain soon．好像马上就要下雨了。

二、feel like＋物质名词，意为“摸上去像是……”。

1. I'm holding something that feels like a potato. 我拿的东西摸上去像个土豆。

2. This kind of brick feels like wood. 这种砖摸起来像木头。

三、feel like＋名词／代词，意为“觉得想做……”。

I feel like a rest after the long journey. 长途旅行后我想休息一下。

四、feel like＋doing，意为“想做……”。

1. I don't feel like walking very much today. 我今天不太想散步。

2. She really feels like having a talk with him about his study at school. 她的确想和他谈一下他在学校的学习情况。

3. I don't feel like eating anything now. 我现在什么都不想吃。

4. Sometimes when I look into the sky, I feel like making a trip somewhere. 当我看天空时，我很想到某个地方旅行。

五、feel like＋反身代词，意为“感到舒适；感觉身体好”，like可省略