Digital controllers for trajectory control of a robot arm are proposed in this paper. A simple discrete-time model of the robot arm obtained by an Euler approximation is used for the design of the controller. Disregarding computation delay in the controller, we derive an algorithm based on the computed torque method. The feedback gains can easily be determined to obtain desired closed loop poles. Using a state predictor, we modify the algorithm so as to take account of unit computation delay. A simulation example shows that the modified algorithm provides better performance for the high gain feedback case. In addition, for the robot arm stabilized by the modified algorithm, we propose a design of an iterative learning controller. The proposed controller consists of a simple error-correction algorithm and a series compensator of FIR type. A simulation example is presented to illustrate the performance of the proposed iterative learning controller.