Aiming at the distributed convex optimization problem in multi-agent systems, a zero-gradient-sum optimization algorithm based on an adaptive event-triggered mechanism is proposed in this paper. An adaptive event-triggered condition is designed based on the virtual clock, and the condition is triggered only when the virtual clock of each agent meets the condition, which effectively reduces the update times of the controller and the communication burden of the system. It is proved that the states of all agents converge asymptotically to the global optimal solution under the algorithm by constructing the Lyapunov function. In addition, the designed event-triggered condition makes the minimum inter-event time designable, effectively excluding Zeno behavior. Finally, the simulation results verify the effectiveness of the algorithm.