<p>We propose a mathematical model describing the tumor-induced angiogenesis, where the role of a matrix metalloproteinase, i.e., the matrix metalloproteinases-2 as a matrix degradation enzyme is considered. The studied mathematical model shows the dynamics of endothelial cells, fibronectin, tumor angiogenesis factor, and matrix degradation enzymes. Besides, we consider both the proliferation and death terms for the dynamics related to the density of endothelial cells. In addition, we numerically investigate this phenomenon in oncology, where a meshless technique in space and a semi-implicit scheme in time is applied to construct a new discrete form. Indeed, a Galerkin weak form of the extended model is gained. Then, we chose both the shape functions of moving least squares approach as the trial and test functions. Additionally, the triangular background cell with a high-order formula to compute the obtained integral terms is employed, allowing us to implement the present global weak form on diverse geometries easily. The well-known row-sum technique is proposed for diagonalizing the mass matrix to facilitate eigenvalue stability. Accordingly, a first-order semi-implicit backward difference formula is applied to find the full-discrete problem, which is solved via a Krylov subspace method, i.e., the biconjugate gradient stabilized algorithm with a proper preconditioner based on a zero-fill incomplete lower-upper factorization is utilized. Finally, the expected biological process is explored by presenting numerical simulations on rectangular and circular domains in two dimensions.</p>