This paper focuses on the problem of convex constraint nonlinear equations involving monotone operators in Euclidean space. A Fletcher and Reeves type derivative-free conjugate gradient method is proposed. The proposed method is designed to ensure the descent property of the search direction at each iteration. Furthermore, the convergence of the proposed method is proved under the assumption that the underlying operator is monotone and Lipschitz continuous. The numerical results show that the method is efficient for the given test problems.