Forward-backward sweep approach is used to solve optimal control problems utilizing a collocation hybrid second derivative block method using polynomial approximate solution via pontryagin's principle. The block method is formed from the discrete linear multistep methods. Also, the forward algorithms, backward algorithm written. The stability properties of the block method are analyzed and proved to be stable, convergent and of order 6. The algorithm is implemented with a written MATLAB code, and three optimal control problems are solved to test the accuracy of the approach, which the numerical examples show that forward-backward sweep methods together with block method via Pontryagin's principle are more accurate when solving optimal control problems than the existing traditional classical Runge-Kutta method. This research work therefore established that block method can be combined with forward backward sweep method using Pontryagin's principle to solve optimal control problems, to produce more accurate result than using the traditional classical Runge-Kutta method.