To make a historical record for Peter of his encounter with Christ and that ultimately people who would read it would believe, might repent, and then put their trust in Christ.
The date Mark's Gospel was written coincides with the end of the First Roman-Jewish War, so it is also plausible that the War was the reason for writing this gospel. It could be that the traumatic events leading up to the time of writing really did seem as if the world was about to end, just as Mark says in chapter 13. The reason that the gospel of Mark was written down was to make a historical record for Peter of his encounter with Christ and that ultimately people who would read it would believe, might repent, and then put their trust in Christ. Otherwise there is no good reason to accept the attribution of Mark's Gospel to the apostle Mark.   Mark, who wrote the Gospel of Mark, was a Christian Jew. He was related to Barnabas and a friend of Peter. Mark is the same person that accompanied the apostle Paul during some of his missions and was referred to as John Mark (Acts 12:12, 25; 15:77-41). John Mark is the same person who is the author of the gospel of Mark even though it could actually be called the gospel of Peter. Peter is believed to have been his mentor after Christ ascended into heaven. Mark was also known as John Mark and sometimes referred to as John Marcus and was apparently the nephew of Barnabas. Mark was the writer of the gospel bearing his name but Peter is actually the one behind the gospel. It is only Mark who wrote down what Peter experienced during his time with Christ. -using Roman time. -explaining Jewish customs Since we now know that Mark's Gospel was the first New Testament gospel to be written, a simple reason could be that it seemed necessary to write down a record of the events in the mission of Jesus before they were forgotten. Mark's gospel was written to a Jewish audience. It is believed that Matthew and Luke took much of their gospels from information provided in the gospel of Mark. The gospel of Matthew, Mark, and Luke were all written to a Jewish audience and much of the wording mirrors one another.
http://www.answers.com/Q/Why_was_Mark%27s_gospel_written http://www.patheos.com/blogs/christiancrier/2014/04/11/what-is-the-purpose-behind-the-gospel-of-mark-a-bible-study/ http://www.answers.com/Q/Why_is_Mark%27_gospel_important_to_Christians http://www.patheos.com/blogs/christiancrier/2014/04/11/what-is-the-purpose-behind-the-gospel-of-mark-a-bible-study/ http://www.patheos.com/blogs/christiancrier/2014/04/11/what-is-the-purpose-behind-the-gospel-of-mark-a-bible-study/ http://www.answers.com/Q/Why_was_Mark%27s_gospel_written http://www.answers.com/Q/Why_was_Mark%27s_gospel_written
explain reasons why mark gospel was needed