An important aspect of cancer biology is cell migration, which is often mediated by chemical gradients in the environment. Three-dimensional (3D) epithelial culture models utilizing biological based matrices such as Matrigel (a popular biomatrix hydrogel) provide a more physiologically relevant setting for studying cancer cell migration. In this paper, we consider a mathematical model of cancer cell migration on a tissue like matrix, which focuses on the response of single MDA-MB-231 (a breast adenocarcinoma cell line) to a concentration gradient of epithelial growth factor (EGF). The domain of interest consists of a water-like medium layer on top of a Matrigel layer. The diffusion of EGF concentration throughout the domain was solved by a finite element method. The diffusion coefficient of EGF in medium was calculated via a previously developed empirical formula while that in Matrigel layer was estimated after a careful study on the characteristics of thin two-layer diffusion problem. An empirical relationship between cell migration rate and the growth factor gradient was developed based on the previous experimental results obtained by our group. The Lagrangian cell migration was then numerically calculated from the modeled cell migration rate. The cell migration results obtained from numerical computations shows an agreement with experimental results.