In this work, we employ the modified form of homotopy perturbation method or shortly ( HPM ) to obtain exact solutions for systems of Volterra integral equations of the second kind. This modification is based on the existens of Taylor expansion of the kernel and source terms. The efficiency and the ability of the approach will be shown by applying the procedure on some examples. If an exact solution exists for the problem, then the obtained series of the solution converges rapidly to that solution.