Cells have a tendency to move toward chemoattractants in the presence of chemical gradients. This characteristic is termed chemotaxis, which is engaged in various biological events such as embryogenesis, wound healing, and immune surveillance. Despite the importance of such a phenomenon, detailed mechanisms have remained unknown. To achieve insights for understanding of chemotaxis, we derived a mathematical model for chemotaxis. In particular, a research motivation for this study is focused on invasive breast cancer cell line MDA-MB-231 under epidermal growth factor (EGF) gradient. Numerical results and analytical investigations demonstrate that signal to noise ratio is related to directionality of migrating cells. To verify the model, we designed an experimental setup using a microfluidic device. Fibrin gel in a microfluidic chip reconstructed 3D environment, and a chemical gradient of EGF was maintained. This model can be useful for investigating chemotactic migration on a cellular level.