This paper presents an adaptive speed swarm control algorithm (ASSC) for autonomous underwater vehicles (AUVs) based on Voronoi topological neighborhoods. The method adopts a leader–follower scheme grounded in agent behaviors and constructs an adaptive tuning factor based on the topological neighbor count and the local Voronoi cell density to dynamically regulate the desired speed of each agent. A virtual spring and damper term with a smoothed distance coefficient is introduced to model attraction–repulsion between agents. Together with a heading alignment term, this yields a distributed control law. Under this model, the swarm achieves cooperative navigation along a sinusoidal trajectory using only local information and does not require global state information. Simulation results demonstrate that the proposed approach maintains formation connectivity and safe separation while achieving strong group cohesion, thereby validating its feasibility and effectiveness.