A simple and straightforward method is presented for evaluating some singular integrals. According to the existing method (Fox [3]), the functional values at the singular points were extrapolated. In this article, the formula is obtained in such a way that it excludes all singular points. The new formula has another merit. Romberg integration of this formula converges faster than that of Fox’s. Moreover, the method is easily used to evaluate the principal value of the singular integrals considered by Delves [2]. The method is illustrated by suitable examples and compared to some existing results.