In this paper, a sparsity-aware target localization method in multiple-input-multiple-output (MIMO) radars by utilizing time difference of arrival (TDOA) measurements is proposed. This method provides a maximum likelihood (ML) estimator for target position by employing compressive sensing techniques. Also, for fast convergence and mitigating the mismatch problem due to grid discretization, we address a block-based search coupled with an adaptive dictionary learning technique. The Cramer-Rao lower bound for this model is derived as a benchmark. Simulations results are included to verify the localization performance.