<p>Based on the inertial extrapolation technique, this paper presents an inertial hybrid approach to the Wei-Yao-Liu conjugate gradient projection method, tailored for solving large-scale nonlinear convex constrained monotone equations. This method utilizes inertial extrapolation to accelerate the convergence of the algorithm at each iteration, while theoretical analysis confirms that, under reasonable and practical assumptions, our proposed algorithm exhibits global convergence and has a linear convergence rate. Our method generates a search direction that possesses both the sufficient descent property and the trust region property, independently of the line search technique. This derivative-free approach enables efficient resolution of large-scale optimization problems. Extensive numerical experiments attest to the effectiveness and robustness of the proposed method. Furthermore, we expand the application scope of our method to include sparse signal reconstruction and image recovery within the framework of compressive sensing. Performance comparisons confirm the feasibility, effectiveness, and competitiveness of our approach. The proposed method stands out as a valuable contribution to solving nonlinear convex constrained monotone equations and holds potential for further applications in compressive sensing.</p>