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In chapter one, the computational techniques and methods used to solve optimal control problems are classified into direct and indirect methods. The contribution of this research is also addressed in this chapter. In chapter two, states some fundamental concepts of Bernstein polynomials with their properties, derivation of new orthonormal Bernstein polynomial of order eight is addressed in this chapter. In chapter three, contains a direct approximate method to solve quadratic optimal control problem, the concept of state parameterization Via orthonormal Bernstein polynomials are discussed in this chapter and the computational result of some examples are included at the end of the chapter. In chapter four, discusses the important conclusions and suggests some recommendations for future work.