The collision risk assessment of multi-ship encounters in busy waters is of great significance for collision risk early warning and the intelligent supervision of maritime traffic. In this paper, a quantitative and visual evaluation method is proposed to describe changes in multi-ship collision risk in the velocity space according to multi-ship collision risk characteristics. Non-linear velocity obstacles and closest point of approach were combined to measure the risk of ship collision from the perspective of both the difficulty and urgency of the encounter. The proposed method was verified via case studies using historical Automatic Identification System data for the East China Sea. The method advantages were confirmed via comparison to the conventional time-varying collision risk and collision risk index methods. The results show that the proposed method can quantify changes in multi-ship collision risk more intuitively and effectively. The proposed method could be further developed as a new risk indicator for maritime traffic safety management and could aid in the navigation safety of manned and unmanned ships.