In this paper, the distributed optimization problem is investigated for a class of general nonlinear model-free multi-agent systems. The dynamical model of each agent is unknown and only the input/output data are available. A model-free adaptive control method is employed, by which the original unknown nonlinear system is equivalently converted into a dynamic linearized model. An event-triggered consensus scheme is developed to guarantee that the consensus error of the outputs of all agents is convergent. Then, by means of the distributed gradient descent method, a novel event-triggered model-free adaptive distributed optimization algorithm is put forward. Sufficient conditions are established to ensure the consensus and optimality of the addressed system. Finally, simulation results are provided to validate the effectiveness of the proposed approach.