In this paper, we are concerned with the problem of solving nonlinear monotone equations with convex constraints in Euclidean spaces. By combining diagonal Barzilai-Borwein method, hyperplane projection method, and adaptive extrapolation technique, an adaptive projection method is constructed. This new method is globally convergent under the assumption of continuity of the underlying map and nonemptiness of the solution set. If this map is Lipschitz continuous and satisfies the local error bound condition, this algorithm has local linear convergence rate. Numerical results show the efficiency of the proposed algorithm.