The conventional step-size scaler (SSS) normalized least-mean-square algorithm is robust against impulsive noise. However, the constant parameter in the SSS needs to be controlled to satisfy the conflicting requirements of fast convergence rate and low steady-state misadjustment. Therefore, to address this problem, an adaptive approach for the parameter in the cost function is proposed in this brief. The proposed approach is then tested in system identification and acoustic echo-cancelation scenarios, which have demonstrated that the proposed approach is effective and robust against non-Gaussian impulsive interferences.