Fitting the huge number of pilots needed for massive multiple inputs multiple outputs antennas (MIMO) channel estimation within the time and frequency resources is a challenging problem. Generally, compressed sensing (CS) channel estimation algorithms face the dilemma of trading off the estimation accuracy and the computational complexity. In this paper, we propose a weighted fast iterative shrinkage thresholding algorithm (W-FISTA). The proposed algorithm provides higher estimation efficiency with the same complexity as the original FISTA. With low computational complexity, multiple measurement vectors (MMV) version of the W-FISTA is proposed to estimate the 3D massive MIMO channel. The proposed MMV-WFISTA estimate the channel coefficients by exploiting its joint sparsity structure in the angle-delay sparse domain. The complexity analysis and the simulation results indicate a clear improvement in the performance of the proposed MMV-WFISTA over joint estimation algorithms.