This paper describes a new type of learning control method for precision velocity control of servomotors suffering from significant disturbance torque. The disturbance torque under consideration is assumed to be periodic in time and nonlinear in system states, but possibly non-Lipschitzian. Based on the property that the learning system tends to oscillate in the steady state, the proposed learning algorithm iteratively generates a feedforward input to cancel the effect of the disturbance torque. Thereby, it can eventually drive the steady-state velocity error to zero. In order to demonstrate the generality of the proposed method, we present a rigorous analysis for the convergence of the proposed learning algorithm. The effectiveness of the proposed method is demonstrated by simulation and experiment.