This paper presents a systematic way of decomposing a limited memory influence diagram (LIMID) to a tree of single-stage decision problems, or submodels and solving it by message passing. The relevance in LIMIDs is formalized by the notion of the partial evaluation of the maximum expected utility, and the graph separation criteria for identifying submodels follow. The submodel decomposition provides a graphical model approach for updating the beliefs and propagating the conditional expected utilities for solving LIMIDs with the worst-case complexity bounded by the maximum treewidth of the individual submodels.