In this paper, we present a modified spectral memoryless quasi-Newton method for solving unconstrained optimization problems. The proposed method is based on the symmetric rank-one (SR1) update, which introduces a rank-one correction to the inverse Hessian approximation. To enhance efficiency and robustness, the method employs a non-quadratic spectral parameter derived from gradient information. This parameter approximates curvature information without the need to store or update full matrices, significantly reducing computational cost and making the method suitable for large-scale problems. A key feature of the proposed algorithm is its ability to preserve the descent property of the search direction at each iteration. This is ensured by incorporating a line search procedure that satisfies the strong Wolfe conditions, thereby improving stability and convergence reliability. Theoretical analysis demonstrates that, under standard assumptions, the algorithm converges globally to a stationary point. Extensive numerical experiments conducted on benchmark test functions show that the proposed method is competitive with, and often superior to, several state-of-the-art optimization methods in terms of convergence speed, robustness, and accuracy.