The normalized subband adaptive filter (NSAF) has a faster convergence rate than the normalized least mean square (NLMS) algorithm for correlated inputs, and its computational complexity is close to that of the NLMS. However, the NSAF suffers from a tradeoff between fast convergence rate and low steady-state misalignment. To address this problem, in this paper we propose a shrinkage variable regularization matrix NSAF (SVRM-NSAF). Its computational complexity almost does not increase compared to the NSAF. The proposed algorithm is derived by minimizing the powers of the noise-free a posterior subband errors. In order to estimate the required noise-free a posterior subband errors, an l₁-l₂ minimization method is used. Simulation results show that the proposed algorithm can obtain both fast convergence rate and low steady-state misalignment.