High resolution Synthetic Aperture Radar (SAR) images are affected by speckle noise, which considerably reduces their visibility and complicates the target identification. In this paper, a new Compressive Sensing (CS) method is proposed to reduce the speckle noise effects of complex valued SAR images. The sparsity of the SAR images allows solving the CS problem using Multiple Measurements Vector (MMV) configuration. Therefore, a special weighted norm is constructed to solve the optimization problem, so that the Variance-Based Joint Sparsity (VBJS) model is used to calculate the weights. An efficient Alternating Direction Method of Multipliers (ADMM) is developed to solve the optimization problem. The obtained results using raw complex-valued measurements with ground truth demonstrate the effectiveness of the proposed despeckling method in terms of both image quality and computational cost.