<p>In this paper, we propose an improved HZ conjugate gradient method with inexact projections for solving large-scale convex-constrained nonlinear equations, based on the feasible inexact projection technique. The search direction generated by the proposed method has the sufficient descent and trust region properties independent of line searches. Under mild conditions, we establish the global convergence of the proposed method without monotonicity or Lipschitz continuity of the underlying mapping. Furthermore, assuming the local Lipschitz continuity, we derive convergence-rate and iteration-complexity bounds for the algorithm. To the best of our knowledge, under assumptions comparable to prior work on inexact projection algorithms, our analysis complements existing results. Numerical experiments on standard nonlinear equations and constrained absolute value equations demonstrate the efficiency and robustness of our method relative to several state-of-the-art algorithms in the literature.</p>