In this study, we have classified well known 20 News Group Set that contains 20.000 documents with a Naïve Bayes Classifier. Rather than using traditional Naïve Bayes method, we have used logarithm based classifier that is more suitable for information retrieval tasks. We successfully evaluated the performance of our implementation using two other classification studies (Icsiboost-bigram and EM) on the same dataset. The performance was measured by comparing it's with the accuracies of other algorithms using the same dataset. We conclude that the Naïve Bayes Classifier performs well among other similar classifiers but it also has its short comings as well.