Abstract: In order to address the clustering consensus problem of a class of nonlinear multi-agent systems with unknown models under a directed topology structure, a model-free clustering consistency control algorithm based on gradient descent is proposed. This approach takes into account the issues of slow convergence in the traditional model-free adaptive control （MFAC） algorithm. First, the adaptive moment estimation （Adam） gradient descent optimization method is introduced into the model-free algorithm. This allows the learning rate to be adaptively adjusted, and the pseudo-partial derivative in MFAC is updated using moment estimates of the gradient, which speeds up convergence and improves the model's accuracy. Next, the multi-agent clustering error is defined under the constraints of system topology and clustering coupling strength. Based on this, a multi-agent clustering consistency control protocol based on Adam-MFAC is designed. Furthermore, the stability and convergence of the Adam-MFAC method are analyzed and proven. Finally, the system with fixed topology and switching topology is considered to simulate the proposed method, and the effectiveness and superiority of the proposed control strategy on the multi-agent clustering consensus problem are demonstrated.