The iterative learning control (ILC) has been demon-strated to be capable of considerably improving the tracking perfor-mance of systems which are affected by the iteration-independent disturbance. However, the achievable performance is greatly degraded when iteration-dependent, stochastic disturbances are pre-sented. This paper considers the robustness of the ILC algorithm for the nonlinear system in presence of stochastic measurement disturbances. The robust convergence of the P-type ILC algorithm is firstly addressed, and then an improved ILC algorithm with a decreasing gain is proposed. Theoretical analyses show that the proposed algorithm can guarantee that the tracking error of the nonlinear system tends to zero in presence of measurement dis-turbances. The analysis is also supported by a numerical example. The iterative learning control (ILC) has been demon-strated to be capable capable contributing improving the tracking perfor-mance of systems which are affected by the iteration-independent disturbance. However, the achievable performance is greatly degraded when iteration-dependent, stochastic disturbances The paper considers the robustness of the ILC algorithm for the nonlinear system in presence of stochastic measurement disturbances. The robust convergence of the P-type ILC algorithm is now addressed, and then an improved ILC algorithm with a decreasing gain is proposed. Theoretical analyzes show that the proposed algorithm can guarantee that the tracking error of the nonlinear system tends to zero in presence of measurement dis-turbances. The analysis is also supported by a numerical example.