In this Letter, a robust variable step-size affine-projection subband adaptive filter algorithm (RVSS-APSAF) is proposed, whereby a band-dependent variable step-size is introduced to improve convergence and misalignment performances in impulsive noise environments. Specifically, the weight vector is adaptively updated to achieve robustness against impulsive noises. Finally, the proposed RVSS-APSAF algorithm is tested for system identification in an impulsive noise environment.