Abstract: For sparse recovery of underdetermined linear systems where noise perturbations exist in both the measurements and sensing matrix, based on FOCal Underdetermined System Solver (FOCUSS) algorithm, an improved algorithm, named Synchronous Descending (SD) FOCUSS, is proposed. The objective function of system model is deduced through a Maximum A Posteriori (MAP) estimation; then approximate optimum sparse-solution can be found while optimizing objective function using iterative relaxation algorithm. Another breakthrough of SD-FOCUSS is that the new algorithm can be applied to Multiple Measurement Vector (MMV) models. The convergence of SD-FOCUSS algorithm can be established with mathematical proof. The simulation results illustrate advantages of the new algorithm on accuracy and stability compared with other algorithms.