This paper proposes a kind of proportional-derivative-type(PD-type) iterative learning control method of accelerated modifying the initial state error for a class of multi-input and multi-output linear time-invariant system. The special time intervals, which can effectively shrink with the increasing of the iterations number, is designed for the system with any initial states. In this interval, the initial state deviation is corrected by using some control algorithm, while in the
outside of the interval, the algorithm is the same as the one for the system without the initial state error. When the error is tracked in the sense of Lebesgue-?? norm, the monotone convergence of the presented learning control is proved by a generalized Young inequality. Numerical simulation results show the effectiveness of the control law.