In this brief, a robust shrinkage normalized sign (RSHNS) algorithm is presented, which uses an optimal step size by minimizing the energy of the noise-free a posteriori error signal and using Price's theorem. To reduce the impact of impulsive noise, the noise-free error signal is estimated by using the robust shrinkage method. It uses two threshold parameters as compared to that in the conventional shrinkage method. Finally, the improved convergence performance of the proposed RSHNS algorithm is demonstrated through simulation results in system identification and echo-cancellation applications.