Nowadays, e-mail is widely becoming one of the fastest and most economical forms of communication but they are prone to be misused. One such misuse is the posting of unsolicited, unwanted e-mails known as spam or junk e-mails. This paper presents and discusses an implementation of a spam filtering system. The idea is to use a neural network which will be trained to recognize different forms of often used words in spam mails. The Bayesian ANN is trained with finite sample sizes to approximate the ideal observer. This strategy can provide improved filtering of Spam than existing Static Spam filters.