In this thesis, an efficient and effective method for finding the solution of optimal control of time delay systems with quadratic cost functional is proposed. This method is based upon hybrid functions approximations. At the beginning, hybrid functions which consist of Block-pulse functions plus Chebyshev polynomials are presented and their properties are discussed. Then, the associated operational matrices of integration, delay, and product are utilized to reduce the solution of optimal control problem to the solution of algebraic equations that is easier than solving the original problem. These matrices have many zeros; hence make the computations very attractive, while preserving the accuracy of the solution. In the mean time, various illustrative examples are included to demonstrate the validity and applicability of the proposed method and the results obtained by present method are compared with those of some other methods. Also, it is shown that the approximate solutions obtained by the present method in some of the mentioned examples satisfy the necessary conditions of optimality for time delay systems up to the required accuracy.