Aiming at the issue of poor robustness of multiple-input multiple-output (MIMO) radar detection caused by the initial clutter estimation error, a joint robust optimization approach of transmitted waveform and received weight is proposed here to improve MIMO radar detection robustness. With the constraints of clutter error convex set, the transmitted waveform constant envelop characteristic and the similarity, the min-max joint optimization problem can be firstly constructed to improve the worst-case detection performance of MIMO radar on the basis of the criterion of maximizing the output signal to interference noise ratio (SINR); After that, in order to solve the resultant NP-hard problem, this issue is decomposed into the internal and external sub-problems, and these two sub-problems can be solved alternately. In comparison with the non-robust and existing robust algorithms as well as unrelated signals, numerical simulation verifies the efficacy of the developed approach.