In this paper, a sparse recovery algorithm based on a double-pulse FDA-MIMO radar is proposed to jointly extract the angle and range estimates of targets. Firstly, the angle estimates of targets are calculated by transmitting a pulse with a zero frequency increment and employing the improved l 1 -SVD method. Subsequently, the range estimates of targets are achieved by utilizing a pulse with a nonzero frequency increment. Specifically, after obtaining the angle estimates of targets, we perform dimensionality reduction processing on the overcomplete dictionary to achieve the automatically paired range and angle in range estimation. Grid partition will bring a heavy computational burden. Therefore, we adopt an iterative grid refinement method to alleviate the above limitation on parameter estimation and propose a new iteration criterion to improve the error between real parameters and their estimates to get a trade-off between the high-precision grid and the atomic correlation. Finally, the proposed algorithm is evaluated by providing the results of the Cramér-Rao lower bound (CRLB) and numerical root mean square error (RMSE).