I 'm looking forward to you go back.这句话有语法错误吗？

有错，因为look forward to 后面跟名词，那个to不是动词不定式里面那个to，而是作为介词，介词后面跟名词，

应该改为：I'm looking forward to your going back.

I 'm looking forward to you going back.
looking forward to 词组
going back 分词形式做名词状语。

look forward to + doing 盼望。。。（固定搭配）

正确的为：I 'm looking forward to you going back.

梁希的答案正确