The aim of this thesis is to provide a clear understanding of some branch of applied mathematics, called optimal control system in O.D.E's and to develop some numerical procedure based on theoretical aspect to solve some class of this field approximately. The motivation and problem formulation of class of optimal control problems have been proposed. The necessary conditions for optimality (if any) have been discussed. A non-classical variational approach for solving some class of control and optimal control problems have been developed and proposed and supported by useful remarks. A numerical procedure based on the non-classical variational approach for solving class of optimal control problems has been developed. A numerical solution using the proposed numerical procedure for solving some optimal control problems including linear and nonlinear optimal control problems with equality and inequality constraints on the control and states of the systems have been implemented and the concerned numerical results have also been obtained. The comparison between the numerical results of the proposed procedure and the exact solutions (if any) or with other numerical results have been shown. The superiority of our results have been obtained even for a low degree of the selected bases using in the approximation sense of the given problem and as one can see in the related sections.