This paper presents a successive approximation approach (SAA) designing optimal controllers for a class of nonlinear systems with a quadratic performance index. By using the SAA, the nonlinear optimal control problem is transformed into a sequence of nonhomogeneous linear two-point boundary value (TPBV) problems. The optimal control law obtained consists of an accurate linear feedback term and a nonlinear compensation term which is the limit of an adjoint vector sequence. By using the finite-step iteration of the nonlinear compensation sequence, we can obtain a suboptimal control law. Simulation examples are employed to test the validity of the SAA.