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In this paper, a modified hybrid three-term conjugate gradient (CG) method is proposed for solving unconstrained optimization problems. The search direction is a three-term hybrid form of the Hestenes-Stiefel (HS) and Liu–Storey (LS) CG parameters. It is established that the method ensures the sufficient descent property independent of line search techniques. The convergence analysis of the proposed method is carried out under standard assumptions for general functions. Numerical experiments on CUTEr problems and image denoising tasks demonstrate that our method outperforms existing approaches in terms of efficiency, accuracy, and robustness, particularly under high levels of salt-and-pepper noise.