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An adaptive least mean M-estimate algorithm for censored regression (CR-LMM) is presented for the robust parameter estimation of the censored regression system. To correct the bias produced by censored observation, the estimated error derived from the probit regression model is employed to construct an M-estimate cost function. It can expel the adverse impact of the impulsive noise and is solved by the unconstrained optimization method. Furthermore, the robust variable step-size (VSS) strategy, which is also predicted on the robust cost function, is also utilized to improve the convergence performance of the proposed CR-LMM algorithm, i.e., convergence speed and steady-state mean square deviation. The condition which guarantees the CR-LMM algorithm stability is obtained by analyzing the convergence in the mean and mean-square sense, and the theoretical steady-state result is also derived. Computer simulations in system identification scenarios are carried out to demonstrate that the proposed algorithms are superior to the existing algorithms in the impulsive environment with different background noise and the theoretical results are verified. [ABSTRACT FROM AUTHOR]