The existing variable step-size convex combination of LMS (VSCLMS) algorithm needs to predetermine the behavioral parameters. To avoid this, the paper proposes a new variable step-size adaptive filter with analytical minimization of the ensemble-averaged mean-square weight error. Instead of variable step-size parameters in the original VSCLMS, the proposed algorithm uses a constant step-size parameter derived based on steady-state MSWE minimization. Theoretical analysis and simulations show that the proposed algorithm has a better tracking performance in the presence of noise and in a time-varying and even non-stable environment. Besides, it converges fast and is stable in the convergence process, and is better in these aspects as compared with the original VSCLMS and CLMS algorithms.