how to write a academic appeal letter?
First you need to decide what you want to appeal against, specifically.
Then you should check whether you have sufficient grounds for appeal.
Find out who you should appeal to - who you address your letter to.
As to the letter, it really depends on the purpose of the appeal: this could range from an appeal against an unfair grade, to an appeal against rejection from entry into a course.
Perhaps if you posted more details, we could help.