This paper discusses the optimal hand trajectories generation for a space robot manipulator. On the topic, the analytical optimal solution exists only for a simplified mathematical model. For the practical case where mass and moment of inertia of links are taken into account, large-dimensional non-linear two point boundary value problem must be solved to obtain the optimal hand trajectory. In this numerical approach, iterative calculation is required to improve the accuracy of solution that takes too much time and cost. In this paper new optimization algorithm by the method of Dynamic Programming (DP) is proposed to solve optimal hand trajectories for the general space robot model with a two-joint arm in the two dimensional coordinate system. This method has the advantages reducing the computational time substantially. Comparison with the numerical results by the method of optimal control theory are made to demonstrate the accuracy of the proposed method.