The variable step-size normalized subband adaptive filter (NSAF) with a fixed parametric step-size scaler (SSS) results in a tradeoff between the fast convergence rate and small steady-state error, and needs to reset the algorithm to improve the tracking in abrupt change scenarios. Thus, a combinedstep-size NSAF with a variable-parametric SSS (VPSSS) is proposed in this brief to address these problems. In the proposed algorithm, an adaptive parameter with respect to the smallest L₁-norm of the subband error vectors in a window is proposed for the VPSSS and then two different step sizes are adaptively combined by a modified sigmoidal activation function, in which this modified sigmoidal activation function is updated by using the gradient descent method to minimize the L₁-norm of the subband error vector. Simulation results have verified that the proposed algorithm yields improved transient behavior and tracking performance as compared to the compared algorithms.