In MIMO radar, existing sparse imaging algorithms commonly vectorize the receiving data, which will destroy the multi-dimension structure of signal and cause the algorithm performance decline. In this paper, the sparsity characteristic and multi-dimension characteristic of signals are considered simultaneously and a new compressive sensing imaging algorithm named tensor-based match pursuit (TMP) is proposed. Firstly, MIMO radar tensor signal model is established to eliminate "dimension disaster". Then, exploiting tensor decomposition to process tensor data sets, tensor-based match pursuit is formulated for multi-dimension sparse signal recovery. Simulation results validates that the proposed method can accomplish high-resolution imaging correctly compared with conventional greedy sparse recovery algorithms. Additionally, under fewer snapshots condition, RMSE of proposed method is lower than other sparse recovery algorithms.