Biodegradable polymer drug-loaded vascular stents are a typical and promising application in the field of invasive interventional therapy. The drug release process of drug-loaded vascular stents, as well as the drug concentration in the vascular wall and its change process, will affect the therapeutic effect of vascular stents on vascular stenosis. As a drug carrier, the degradation properties of the polymer will affect the drug release process. In this study, the drug release process from the biodegradable polymer stent and the drug delivery process in vascular lumens and intravascular walls were studied by using 3D finite element method, with the effect of the biodegradation behavior of polymer on the drug release process being considered. The effects of the initial drug concentration, stent geometry, and polymer degradation rate on the drug release and delivery process were investigated. The results showed that the initial drug concentration and the thickness of the polymer stent significantly affected the drug concentration in the middle layer of the vessel wall, but the initial drug concentration had no effect on the drug release duration. The degradation of the polymer causes its porosity to change with time, which affects the drug diffusion in polymer, and further affects the drug concentration in the vessel wall. The three-dimensional structure of the stent can affect the blood flow in the blood vessel, resulting in drug deposition near the struts, especially near the intersection of the support struts and the bridge struts.