A novel zero attraction affine projection sign algorithm (ZA-APSA) for strong impulsive and sparse environment is proposed in this paper. Here norm penalty is introduced to original cost function of APSA which provides zero attraction to the filter weights. The APSA provides lower computational complexity and is robust against impulsive noise, whereas the ZA-APA works well in sparse environment with improved convergence and lower steady-state error. The proposed ZA-APSA combines the feature of APSA and ZA-APA, and hence, it provides faster convergence and lesser steady-state error with high robustness to impulsive interference with low computational complexity than the conventional ones. The stability condition for the convergence in the mean and mean square error sense is derived. Theoretical analysis is made to prove that the proposed algorithm can achieve lesser steady-state mean square error than APSA. Simulations are performed to validate the analysis made and to prove the suitability of the proposed algorithm for sparse and impulsive system identification.