A convex regularized variable-forgetting-factor recursive least squares algorithm (CR-VFFRLS) is proposed for sparse system identification, in which the variable-forgetting-factor is deduced by minimizing the convex regularized cost function via the gradient descent method. It overcomes the drawback that the fast-tracking ability with the high steady-state error or the low steady-state error with slow tracking ability, which is ineluctable in the fixed forgetting-factor RLS algorithm. Simulation results demonstrate the superiorities of the proposed algorithm to the CR-RLS and VFFRLS algorithm.