•Based on the encounter evolution, a method is proposed to enable the construction of a ship collision risk model.•A PVO model is developed with an elliptic conflict region, utilizing ddv and tdv to quantify state risk of velocities.•A collision risk evolution model is introduced, incorporating spatial attributes, macro-level and micro-level decisions.•Historical scenarios and encounter stages are employed to determine model parameters and their weights. Aiming at realizing collision risk quantitative evaluation among encounter ships, a novel data-driven evolution model is proposed concerning encounter evolution in maritime transportation. A probabilistic velocity obstacle with an elliptic conflict region is constructed by taking into account uncertainty. The degree of and time to domain violation are introduced to quantify collision risk levels under varying velocities. Then, a ship collision risk evolution model is formulated by considering spatial attributes, macro-level and micro-level evolution based on a realistic collision avoidance decision. The model parameters and their weights are determined by statistical analysis of historical encounter scenarios and the characteristics of encounter stages. Therefore, the model encapsulates the statistical characteristics of actual data, which improves its practical values. The results of case studies indicate that the collision risk evolution model can properly reflect collision risk, so that collision evolution stages can be classified accordingly for rational anti-collision guidance. It brings new contributions to risk visualization, collision avoidance decision-making, and collision accident analysis and responsibility determination.