The rapid growth of Internet of Things (IoT) and 5G technologies has led to a sharp increase in computing demands from wireless devices, making efficient task offloading a critical challenge. Key issues include reducing application latency, lowering the energy consumption of terminal devices, and improving overall system performance, all of which directly affect user experience. Traditional genetic algorithms (GA), inspired by biological evolution, have been widely used in task offloading, but they often suffer from slow convergence and a tendency to fall into local optima in complex scenarios, limiting their effectiveness. To address these drawbacks, this paper proposes a task offloading strategy based on a refined elite mechanism in a GA. The algorithm introduces multi-point variation in both crossover and mutation operations to enhance population diversity, avoid local optima, and accelerate convergence. This design leverages the GA’s strength in multi-objective optimization, which outperforms other bionic heuristic algorithms that excel in single domains. Comparative experiments with GA, ant colony optimization, Deep Q-Network, Greedy algorithms, simulated annealing algorithm and particle swarm optimization, show that the proposed algorithm improves convergence speed by 35%, reduces task completion time by 6%, and optimizes energy consumption by approximately 18%.