In this work, an optimal control strategy for a robot manipulator is proposed based on Iterative Sequential Action Control (ISAC). Firstly, the robot manipulator system is described as the Euler-Lagrange form, generating a nonlinear dynamic system. Then, based on the ISAC algorithm, an analytic optimal control method for the robot manipulator system is proposed, which is composed of the dynamics prediction, the analytic optimal control action derivation, the control application time calculation, and the control duration determination. As the optimal control value is obtained analytically, the proposed method is efficient enough for the online control of the robot manipulator. Finally, the simulation experiments are designed and conducted. Simulation results verify that the proposed analytic optimal control method has fast response speed, high control precision, and good stability.