This paper proposes a new order reduction approach for Roesser state-space model based on elementary operations, by inversely applying the basic idea adopted in the well-known elementary operation approaches to the Roesser state-space model realization of multidimensional (n-D) systems. It will be shown first that the order reduction problem can be formulated into an elementary operation problem of an initial n-D polynomial matrix constructed by the coefficient matrices of the given Roesser state-space model. Based on this formulation, a basic order reduction procedure is presented and examples are given to illustrate the details as well as the effectiveness of the proposed procedure.