<p>In this paper, we propose a hybrid accelerated derivative-free projection method for solving nonlinear equations. The acceleration parameter encompasses the convex combination parameter, the inertial parameter, and their hybridization. The three-term derivative-free direction designed has good theoretical properties independent of line searches. Without the Lipschitz continuity of the underlying mapping, we establish the global convergence of the proposed algorithm. Importantly, we demonstrate the local convergence rate of the proposed algorithm under the local Lipschitz continuity condition. Finally, solving benchmark test instances and sparse signal recovery problems demonstrates the effectiveness and robustness of the proposed algorithm.</p>