It is well known that the affine projection algorithm (APA) offers a good tradeoff between convergence rate/tracking and computational complexity. Recently, the evolutionary APA (E-APA) with a variable projection order has been proposed. In this paper, we propose a variable step size (VSS) version of the E-APA, called VSS-E-APA. It is shown that the VSS-E-APA is robust to near-end signal variations. Also, it has both a fast convergence speed and a small steady-state error and a much reduced numerical complexity than the VSS-APA.