Teacher, please check my letter.
I would like to take three weeks' leave from February 4 to 22, 2013 to visit my 80-year old father who lives in Shanghai. I have not seen him for almost three years and wish to spend more time with him. I have two weeks holiday for next year and I will apply for one week unpaid. Please approve my request. Thank you.
Instead of "Please approve etc.", you might say "I respctfully request your approval" and there is no need for an apostrophe with "weeks". Otherwise OK.