Glioblastoma multiforme is one of the deadliest human cancers and is characterized by tumor cells that hijack immune system cells in a deadly symbiotic relationship. Microglia and glioma infiltrating macrophages, which in principle should mount an immune response to the tumor, are subverted by tumor cells to facilitate growth in several ways. In this study, we seek to understand the interactions between the tumor cells and the microglia that enhance tumor growth, and for this purpose, we develop a mathematical and computational model that involves reaction-diffusion equations for the important components in the interaction. These include the densities of tumor and microglial cells, and the concentrations of growth factors and other signaling molecules. We apply this model to a transwell assay used in the laboratory to demonstrate that microglia can stimulate tumor cell invasion by secreting the growth factor TGF- β. We show that the model can both replicate the major components of the experimental findings and make new predictions to guide future experiments aimed at the development of new therapeutic approaches. Sensitivity analysis is used to identify the most important parameters as an aid to future experimental work. This study is the first step in a program that involves development of detailed 3-D models of the mechanical and biochemical interactions between a glioblastoma and the tumor microenvironment.