Tumors exploit angiogenesis, the formation of new blood vessels from pre-existing vasculature, in order to obtain nutrients required for continued growth and proliferation. Targeting factors that regulate angiogenesis, including the potent promoter vascular endothelial growth factor (VEGF), is therefore an attractive strategy for inhibiting tumor growth. Computational modeling can be used to identify tumor-specific properties that influence the response to anti-angiogenic strategies. Here, we build on our previous systems biology model of VEGF transport and kinetics in tumor-bearing mice to include a tumor compartment whose volume depends on the "angiogenic signal" produced when VEGF binds to its receptors on tumor endothelial cells. We trained and validated the model using published in vivo measurements of xenograft tumor volume, producing a model that accurately predicts the tumor's response to anti-angiogenic treatment. We applied the model to investigate how tumor growth kinetics influence the response to anti-angiogenic treatment targeting VEGF. Based on multivariate regression analysis, we found that certain intrinsic kinetic parameters that characterize the growth of tumors could successfully predict response to anti-VEGF treatment, the reduction in tumor volume. Lastly, we use the trained model to predict the response to anti-VEGF therapy for tumors expressing different levels of VEGF receptors. The model predicts that certain tumors are more sensitive to treatment than others, and the response to treatment shows a nonlinear dependence on the VEGF receptor expression. Overall, this model is a useful tool for predicting how tumors will respond to anti-VEGF treatment, and it complements pre-clinical in vivo mouse studies.