Learning English in China, the Chinese English teacher always says it is important to note that the syntax. But I heard that some foreign people will not care much about grammar, As long as can understand each other.Is this true?? (if this have any grammar mistake，please forgive me, my grammar is very poor; -))

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Good question. All I can tell you is what works for me:

Grammar is VERY important, since how you choose to express yourself determines what people think about you. Depending on what impression you want to make, sometimes you'd say things that are correct grammar and sometimes you'd say things that aren't considered correct. But they would still be natural.

Grammer is like looking in the rearview mirror, and much of what is considered "correct" today includes things that were incorrect but very common a generation ago.

To sound really natural, like others have already said, it's critical to imitate real native speech and writing as much as you possibly can.

Personally, I've never been able to get any real benefit out of studying grammar. I have received huge benefits from imitating native speakers.

For example, I take many of the HiNative answers by native speakers and put them in Anki (which is a SRS program) so I can practice them over and over and over... I do the same thing with things that native speakers post on Facebook, or Weibo or 百思不得姐 or whatever.

If you don't mind spending a little money, I've found materials from Glossika very helpful for imitating native speech. http://www.glossika.com/

In the end, this seems to help me learn natural language much better.