In this research, we investigated the nonnegative cone horizontal linear complementarity problem (HLCP). Initially, we transformed the HLCP into a fixed-point equation using the modulus defined within the nonnegative cone. By redefining this fixed-point equation as a monotone system, we introduced an improved multivariate spectral gradient projection method for solving it. This study shows that the proposed iterative method converges to the solution of the HLCP, assuming the specified conditions are met. Additionally, numerical examples were included to illustrate the practicality and effectiveness of the modulus-based enhanced multivariate spectral gradient projection method in computational settings.