Different from previous viewpoints, multivariate polynomial matrix Diophantine equations are studied from the perspective of modules in this paper, that is, regarding the columns of matrices as elements in modules. A necessary and sufficient condition of the existence for the solution of equations is derived. Using powerful features and theoretical foundation of Grobner bases for modules, the problem for determining and computing the solution of matrix Diophantine equations can be solved. Meanwhile, the authors make use of the extension on modules for the GVW algorithm that is a signature-based Grobner basis algorithm as a powerful tool for the computation of Grobner basis for module and the representation coefficients problem directly related to the particular solution of equations. As a consequence, a complete algorithm for solving multivariate polynomial matrix Diophantine equations by the Grobner basis method is presented and has been implemented on the computer algebra system Maple.