The affine projection algorithm (APA) and the normalized subband adaptive filter (NSAF) have been proposed to improve the convergence rate of the normalized least mean square algorithm for colored input signals. Recently, the improved multiband-structured subband adaptive filter (IMSAF) has been advanced, combining the APA and NSAF optimization approaches. The use of the IMSAF may result in accelerated convergence rate but at the expense of a large increase in computational complexity. In this brief, a reduced complexity subband adaptive algorithm is proposed, which employs sparse subfilters and a subband APA cost function. A variable-step-size method is developed, thereby providing fast convergence rate while ensuring small steady-state misadjustment.