As the volume and velocity of Big Data continue to grow, traditional cloud computing approaches struggle to meet the demands of real-time processing and low latency. Fog computing, with its distributed network of edge devices, emerges as a compelling solution. However, efficient task scheduling in fog computing remains a challenge due to its inherently multi-objective nature, balancing factors like execution time, response time, and resource utilization. This paper proposes a hybrid Genetic Algorithm (GA)-Particle Swarm Optimization (PSO) algorithm to optimize multi-objective task scheduling in fog computing environments. The hybrid approach combines the strengths of GA and PSO, achieving effective exploration and exploitation of the search space, leading to improved performance compared to traditional single-algorithm approaches. The proposed hybrid algorithm results improved the execution time by 85.68% when compared with GA algorithm, by 84% when compared with Hybrid PWOA and by 51.03% when compared with PSO algorithm as well as it improved the response time by 67.28% when compared with GA algorithm, by 54.24% when compared with Hybrid PWOA and by 75.40% when compared with PSO algorithm as well as it improved the completion time by 68.69% when compared with GA algorithm, by 98.91% when compared with Hybrid PWOA and by 75.90% when compared with PSO algorithm when various tasks inputs are given. The proposed hybrid algorithm results also improved the execution time by 84.87% when compared with GA algorithm, by 88.64% when compared with Hybrid PWOA and by 85.07% when compared with PSO algorithm it improved the response time by 65.92% when compared with GA algorithm, by 80.51% when compared with Hybrid PWOA and by 85.26% when compared with PSO algorithm as well as it improved the completion time by 67.60% when compared with GA algorithm, by 81.34% when compared with Hybrid PWOA and by 85.23% when compared with PSO algorithm when various fog nodes are given.