For the robustness problem of open-loop P-type iterative learning control under the influence of measurement noise which is inevitable in actual systems,an adaptive adjustment algorithm of iterative learning nonlinear gain matrix based on error amplitude is proposed and two nonlinear gain functions are given. Then with the help of Bellman-Gronwall lemma,the robustness proof is derived.At last,an example is simulated and analyzed. The results show that when there exists measurement noise,the proposed learning law adjusts the learning gain matrix on line based on error amplitude,thus can make a compromise between learning convergence rate and convergence accuracy to some extent:the fast convergence rate is achieved with high gain in initial learning stage,the strong robustness and high convergence accuracy are achieved at the same time with small gain in the end learning stage,thus better learning results are obtained. For the robustness problem of open-loop P-type iterative learning control under the influence of measurement noise which is inevitable in actual systems, an adaptive adjustment algorithm of iterative learning nonlinear gain matrix based on error amplitude is proposed and two nonlinear gain functions are given . Then with the help of Bellman-Gronwall lemma, the robustness proof is derived. At last, an example is simulated and analyzed. The results show that when there exists there measurement noise, the proposed learning law adjusts the learning gain matrix on line based on error amplitude, thus can make a compromise between learning convergence rate and convergence accuracy to some extent: the fast convergence rate is achieved with high gain in initial learning stage, the strong robustness and high convergence accuracy are achieved at the same time with small gain in the end learning stage, thus better learning results are obtained.