In this work we use support vector machine to predict polyadenylation sites (Poly (A) sites) in human DNA and mRNA sequences by analyzing features around them. Two models are created. The first model identifies the possible location of the Poly (A) site effectively. The second model distinguishes between true and false Poly (A) sites, hence effectively detect the region where Poly (A) sites and transcription termination occurs. The support vector machine (SVM) approach achieves almost 90% sensitivity, 83% accuracy, 80% precision and 76% specificity on tests of the chromosomal data such as chromosome 21, The models are able to make on average just about one false prediction every 7000 nucleotides. In most cases, better results can be achieved in comparison with those reported previously on the same data sets.