In this thesis, two numerical methods for finding the solution of time varying linear quadratic optimal control problems with inequality constraints on state and control variables are presented. The first method is based upon hybrid of block-pulse functions and Chebyshev polynomials, which is a new computational method. The properties of hybrid function together with the associated operational matrices of integration and product are used to reduced the optimal control problem to the solution of algebraic equations. The second method is based upon Chebyshev spectral method introduced by Jaddu. This method converts the optimal control problem in to a standard quadratic programming problem. In order to demonstrate the efficiency and accuracy of the new method, a comparison is made between the computational results obtained by hybrid functions and Chebyshev spectral method.