In this study finite part integrals are utilized for evaluation of hypersingular and nearly-hypersingular surface integrals on curvilinear elements. These integrals are related to the second derivative of the free space Green' function and arise in the solution of electric field integral equation (EFIE) via locally corrected Nystriim (LCN) method. The curvilinear elements are represented by the Taylor series expansion of the surface function around the observation point. The hypersingular integral, defined on a curvilinear element, is written as a summation of hypersingular and weakly singular integrals which are defined on a flat surface. Numerical studies show that increased accuracy is obtained for hypersingular integrals on curvilinear elements.