In this paper, a new spectral projection method for solving nonlinear system of equations with convex constraints is proposed based on inertial effect. The inertial technique is integrated into the new proposed search direction with the aim of enhancing the numerical performance. Interestingly, the convergence result of the new method is established based on the assumption that the underlying function is pseudomonotone. This assumption is weaker than monotonicity which is used in many existing methods to prove the convergence. The new method is suitable for large scale problems as well as nonsmooth problems. Numerical experiments presented validate the efficiency of the new method which also outperforms some existing methods in the literature.