Angiogenesis, the formation of new blood vessels, is crucial in both normal and pathological contexts, notably cancer. This complex process involves interactions among endothelial cells, tumor angiogenic factors, matrix metalloproteinases, and inhibitors. In this article, we introduce a preliminary mathematical model of angiogenesis described by a system of partial differential equations. We discretize the model spatially and solve it in time direction using a simple forward method, specifically the Euler method. This approach simplifies the computational process and provides a foundational understanding of the dynamics involved. Numerical tests and results confirm the reliability of proposed numerical procedure.