The issue of robust multi-input multi-output (MIMO) radar waveform design is investigated in the presence of imperfect clutter prior knowledge to improve the worst-case detection performance of space-time adaptive processing (STAP). Robust design is needed because waveform design is often sensitive to uncertainties in the initial parameter estimates. Following the min-max approach, a robust waveform covariance matrix (WCM) design is formulated in this work with the criterion of maximization of the worst-case output signal-interference-noise-ratio (SINR) under the constraint of the initial parameter estimation errors to ease this sensitivity systematically and thus improve the robustness of the detection performance to the uncertainties in the initial parameter estimates. To tackle the resultant complicated and nonlinear robust waveform optimization issue, a new diagonal loading (DL) based iterative approach is developed, in which the inner and outer optimization problems can be relaxed to convex problems by using DL method, and hence both of them can be solved very effectively. As compared to the non-robust method and uncorrelated waveforms, numerical simulations show that the proposed method can improve the robustness of the detection performance of STAP.