In this paper, a real-valued reweighted l₁ norm minimization method based on data reconstruction in monostatic multiple-input multiple-output (MIMO) radar is proposed. Exploiting the special structure of the received data, and through the received data reconstruction approach and unitary transformation technique, a one-dimensional real-valued received data matrix can be obtained for recovering the sparse signal. Then a weight matrix based on real-valued MUSIC spectrum is designed for reweighting l₁ norm minimization to enhance the sparsity of solution. Finally, the DOA can be estimated by finding the non-zero rows in the recovered matrix. Compared with traditional l₁ norm-based minimization methods, the proposed method provides better angle estimation performance. Simulation results are presented to verify the effectiveness and advantage of the proposed method.