In this study, we propose a noisy nonlinear extension of independent component analysis (ICA). There have been proposed several extensions of the original noise-free linear ICA, e.g., noisy ICA or nonlinear ICA. There are few studies dealing with both noisy and nonlinear situations, however, because of the difficulty in integral calculation of the likelihood. In this study, we approximate the integral by a Taylor expansion and a Laplace approximation. The derived algorithm formulated as an expectation-maximization (EM) algorithm generalizes several of existing ICA algorithms. We also obtain an optimal step size for our EM algorithm and discuss the reason why various noisy linear ICA algorithms based on maximum likelihood estimation are unsuccessful in being the noise-free linear ICA in the noiseless limit.