The Grasshopper Optimization Algorithm (GOA) is a metaheuristic algorithm based on the behavior of grasshoppers in swarms. However, in contrast to its advantages, it has some limitations, such as slow convergence, poor exploitation of solutions, and its tendency to get stuck in local optima. To overcome these limitations, this paper presents a novel hybrid model called the Quadratic Self-Organizing Migrating Grasshopper Optimization Algorithm (Q-SOMGOA). This model merges GOA with the quadratic approximation and the self-organizing migrating algorithm, Q-SOMGOA, is proposed. This method was validated through tests on 21 functions and 2 real-life problems, resulting in faster convergence and more accurate results as compared to GOA. The test was evaluated using the Wilcoxon rank-sum test that confirms the superiority of Q-SOMGOA over GOA.