It is about two deacades that study and research concerning wavelets initiaed and have been applied extensively to various fields. The wavelets was initiaed in the early nineteen tens. The most of mathematicians have investigated wavelet analysis from ninteen eighty five. In this thesis a computational method for solving calculus of variations problems and optimal control of systems is presented. The method is based upon Legendre wavelets approximations. The properties of Legendre wavelets are presented. Opperational matrices of integration and product are then utilized to reduce the calculus of variations and optimal control problems to the solution of algebraic equations. Illustrative examples are included to demonstrate the validity accuracy and applicability of the proposed method.