In order to track the desired reference trajectory from an oscillating control system with two delays in a finite time interval, we design iterative learning control updating laws to generate a sequence of input control functions such that the error between the output and the desired reference trajectories tends to zero via a suitable norm in the sense of uniform convergence. Here, we adopt a delayed matrix function to characterize the output state, which can be easily solved in the simulation. As a result, convergence analysis results are given. Finally, simulation results are provided to illustrate the effectiveness of the proposed controllers.