SummaryThis paper presents a new variable step‐size diffusion affine projection algorithm (VSS‐DAPA) to advance the filter performance of the diffusion affine projection algorithm (DAPA). The proposed VSS strategy is developed for the DAPA, which can solve the distributed estimation problem over diffusion networks well. To obtain the optimal step size reasonably, we seek the update recursion of mean‐square deviation (MSD) that is suitable for the DAPA. The step size is optimally given through the minimization for the MSD of the DAPA at each iteration. The derived step size through the MSD minimization improves the filter performance with respect to the convergence and the estimation error in steady state. The results based on simulations demonstrate that the proposed VSS‐DAPA performs better than the existing algorithms with a system‐identification scenario in diffusion network. Copyright © 2015 John Wiley & Sons, Ltd.