This study investigates the Grover Quantum Approximate Optimization Algorithm (G-QAOA) for solving the 3-SAT problem, demonstrating a quadratic speedup over random sampling. G-QAOA is shown to be more resource-efficient and adaptable for 3-SAT and Max-SAT problems compared to Grover's algorithm and conventional QAOA. Classical simulations on thousands of random 3-SAT instances up to 26 Boolean variables with densities ranging from 2 to 8 confirm the quadratic speedup. The single-angle-pair constraint, which uses the same pair of angles across all G-QAOA rounds, significantly reduces classical computational overhead while preserving the quadratic speedup. Parameter clustering is observed, indicating that the angles cluster in a small parameter range across all 3-SAT instances. These findings are further validated on the IonQ Aria quantum computer, where G-QAOA outperforms X-QAOA in terms of solution probability and uniformity. The research highlights the potential of G-QAOA for practical applications in combinatorial optimization and quantum computing.This study investigates the Grover Quantum Approximate Optimization Algorithm (G-QAOA) for solving the 3-SAT problem, demonstrating a quadratic speedup over random sampling. G-QAOA is shown to be more resource-efficient and adaptable for 3-SAT and Max-SAT problems compared to Grover's algorithm and conventional QAOA. Classical simulations on thousands of random 3-SAT instances up to 26 Boolean variables with densities ranging from 2 to 8 confirm the quadratic speedup. The single-angle-pair constraint, which uses the same pair of angles across all G-QAOA rounds, significantly reduces classical computational overhead while preserving the quadratic speedup. Parameter clustering is observed, indicating that the angles cluster in a small parameter range across all 3-SAT instances. These findings are further validated on the IonQ Aria quantum computer, where G-QAOA outperforms X-QAOA in terms of solution probability and uniformity. The research highlights the potential of G-QAOA for practical applications in combinatorial optimization and quantum computing.