A novel hybrid affine projection algorithm (H-APA) is proposed. This algorithm is considered to be a derivation of the affine projection sign algorithm (APSA). The APSA can be greatly affected by impulsive noise. To solve this problem, the proposed algorithm is applied with the robust mixed-norm algorithm (RMNA). The simulated results show that the proposed algorithm is insensitive to impulsive noise with fast convergence rate under the colored input condition. In addition, a simplified H-APA (SH-APA) is derived based on the proposed H-APA to reduce the complexity of the algorithm. Numerical simulations show that compared with the existing AP-type algorithms, the proposed algorithms have faster convergence speed.