This paper considers moving target detection for multiple-input multiple-output (MIMO) radar in compound-Gaussian clutter. A new detector is devised according to a centralized processing scheme for MIMO radar system based on the generalized likelihood ratio test (GLRT) design criterion. Then, an adaptive version of the derived detector is investigated. The fixed point estimation (FPE) strategy is introduced to make the proposed detector fully adaptive. Finally, several numerical simulations of the derived detectors with typical parameters are obtained and discussed.