My salary has increased since Jan 2013. But my work permit still with the previous salary. So I am going to write letter to update it.
Subject: - Request to update salary on Work permit
Dear Sir,
With all due respect, I would like to inform you that my work permit salary is not matching with what I am getting, as my salary has been increased 18 months ago.
My work permit is going to expire three months later. So, it is requested you, please update my new work permit as per my actual salary.
Thank you
Sincerely,

Rather than starting with "Dear Sir," it is more professional to use "Sir/Ma'am:" with the semicolon.

You could skip "I would like to inform you that my work permit salary is not matching with what I am getting, as" and simply inform them of your salary increase.

To make subject and verb agree, you might wish to change the "three months later" to "within three months."

I agree with catsmine's comments. and-
Instead of subject (usually used in internal memos), use Re: (abbrev for Reference identitifying what the letter is in regard to)
Don't forget a date for the letter, (near top of page), which makes all other references to time- more easily understood.
Save the respectfully as a word by itself just before your signature, or simply-"Sincerely"
'I would like..." followed by anything is a very weak use of English and has become a cliche'.
As in "I would like to thank you for ..." Better to say "I thank you for...: "would like to" implies that you never quite got to actually doing it.