In order to accelerate the convergence speed of iterative learning control(ILC) law, taking the PD-type learning law for example, an acceleration correction algorithm with variable gain and adjustment of learning interval is proposed for the linear time invariant(LTI) system. First of all, the modified interval in the next iteration is determined based on the learning effects, and the control law gain is modified in the interval. Then, analysis results show that the convergence speed mainly depends on the system state, the learning gain, the correction exponential and the learning interval in the sense of Lebesgue-p norm. In the same simulation condition, the proposed algorithm has a faster convergence speed compared with the traditional algorithms.