This brief proposes a recursive constrained sine second-order error promoting adaptive (RCSSOEPA) algorithm. Compared with classical recursive method, the RCSSOEPA algorithm can achieve better steady state performance in impulsive noise. In general, the sine second-order error (SSOE) is constructed to devise a new recursive constrained adaptive-filtering within the least-squares framework for solving linear constrained optimization problems. The mean-square (MS) stability of the RCSSOEPA and its theoretical instantaneous MS deviation under Gaussian and non Gaussian noise are analyzed, numerically investigated and discussed in detail. Simulated results are reported to give a comfirmation of the theoretical analysis, and show that the RCSSOEPA outperforms recent developed constrained adaptive filtering algorithms in the estimation misalignment and when used for system identification under impulsive-noise.