This paper proposes a nonparametric variable step-size least mean absolute third (NVSLMAT) algorithm to improve the capability of the adaptive filtering algorithm against the impulsive noise and other types of noise. The step-size of the NVSLMAT is obtained using the instantaneous value of a current error estimate and a posterior error estimate. This approach is different from the traditional method of nonparametric variance estimate. In the NVSLMAT algorithm, fewer parameters need to be set, thereby reducing the complexity considerably. Additionally, the mean of the additive noise does not necessarily equal zero in the proposed algorithm. In addition, the mean convergence and steady-state mean-square deviation of the NVSLMAT algorithm are derived and the computational complexity of NVSLMAT is analyzed theoretically. Furthermore, the experimental results in system identification applications presented illustrate the principle and efficiency of the NVSLMAT algorithm.