Abstract: The conventional affine projection algorithm(APA) converges faster, but it involves high computational complexity.Set membership affine projection algorithm(SM-AP) can effectively reduce the computation due to data-selective update.However it converges slowly due to the use of scalar error.Using the time-varying step size of set-membership filter(SMF), the conventional APA is reformed to a novel affine projection algorithm with variable step-size based on SMF.Compared to the SM-AP algorithm, the proposed algorithm converges faster with vector error, and it features data-selective update as SMF.The performance of the proposed algorithm is verified by the experiments of system identification and echo cancellation.