This paper presents a distributed optimization algorithm for time-varying objective functions utilizing a prescribed-time convergent multi-agent system within undirected communication networks. Departing from conventional time-invariant optimization paradigms with static optimal solutions, our approach specifically addresses the challenge of tracking dynamic optimal trajectories in evolving environments. A novel continuous-time distributed optimization algorithm is developed based on prescribed-time consensus, guaranteeing the consensus attainment among agents within a user-defined timeframe while asymptotically converging to the time-dependent optimal solution. The proposed methodology enables explicit predetermination of convergence duration, representing a significant advancement over existing asymptotic convergence methods. Moreover, two simulation examples on the rendezvous problem and multi-robots control are presented to validate the theoretical results, exhibiting precise time-controlled convergence characteristics and effective tracking performance for time-varying optimization targets.