This paper deals with the problem of detection of distributed multi-input multi-output (MIMO) radar on moving platforms. We consider the detection of targets in compound-Gaussian clutter, describing the clutter consisting speckle and texture components. Furthermore, under effects of platform motion and varied scenarios, one major challenge of detector is clutter non-homogeneity. Due to these clutter models, a novel generalized likelihood ratio test (GLRT) based detector is proposed. With the priori knowledge about matrix taper of the clutter covariance matrix, the detector adopts the Bayesian approach without resorting to training data that is non-homogeneity with the samples under test. To handle with the non-homogeneity of the Doppler frequencies of clutters, the detector employs a nonlinear processing by iteration and reconstruction of sparse signals to estimate unknown parameters. Some simulations are presented to illustrate the superior performance of the proposed detector in thus complicated scenarios.