Hello ndq_quang and thanks for this essay. It's brave of you to tackle a topic like this! 

Introduction

Good clear introduction with both positive and negative sides given and a clear background. Perhaps giving the opinion would help instead of leaving the reader in suspense until the end.

Word Choice

You wrote

• After that, what do people often do?  

And what do people do in this situation? OR
How do people deal with/handle this lack of punctuality? OR
What is the common reaction to lateness? 

You wrote

Moreover, whenever making mistakes, human constantly try to find reason justifying their faults or blame it to other one and so are Vietnamese people → 

Moreover, after making mistakes, people constantly try to justify their actions and blame others, and so do Vietnamese people 
OR  …and Vietnamese people are no exception

• They say sorry carelessly just because it is absolutely normal.

They just apologize casually/ off-handedly / because to them it is absolutely normal and unimportant  OR  
... because to them it seems unimportant

• Fabricate → claim
• How embarrassed is that!→ Ho embarrassing is that!
• What we need to do now is changing ourselves, practice punctuality day by day, from small things to big things 

• What we need to do now is change ourselves by practicing punctuality day by day, from small things to big things OR
• What we need to do now is to practice punctuality daily in small things and big things.

  
  

• On the other hand, almost Vietnamese people surely bear in mind that everyone will come late, so why they need to arrive on time and wait for another.

Here ‘on the other hand’ is not correct. It is used to mean a new opposite or contrary idea, not a related one or a further example  It needs to be replaced with “In addition,” or “In any case,” or “Of course,” or “Naturally,” or “Furthermore,”  or something like this:

And anyway, since everyone is going to come late, what’s the point of being on time [and having to wait for everyone else]?

I like many of the phrases and sentences in your essay. The essay is interesting and the writing shows a sense of style.  Here’s a nice sentence with a magic list of three:

If we can do that, we would show the foreigners that our citizens are hard-working, responsible and professional.

One point (not an English writing point, just an idea) you might consider discussing is why bother changing just to prove something to foreigners? What motivation would Vietnamese have for changing for their own benefit?  

Overall, as I said, an interesting topic well covered. I wonder if anyone else would like to pick a bad habit from their country?!