Recently, the sign subband adaptive filter (SSAF) algorithm has obtained great attention, due to its robustness against impulsive noises and decorrelating property for correlated input signals. However, the performance of the algorithm in the steady-state is not analyzed. In this paper, we study the steady-state mean-square-deviation (MSD) behavior of the SSAF algorithm by using energy conservation relation, Price's theorem and some reasonable assumptions. Simulation results in different system identification scenarios (including the input signals, tap lengths, impulsive noises, number of subbands, and step sizes) are provided to support our theoretical analysis.