The proliferation of emerging applications such as augmented reality, face recognition, and autonomous driving have stimulated the growth of demand for low-latency services, while the traditional cloud computing paradigm inevitably increases end-to-end latency. Multi-access edge computing deploys computing and storage resources to user terminals, which is expected to become an effective solution. Most of the existing researches on multi-access edge computing focus on the offloading of independent tasks, which cannot meet the challenge of a real scenario in which a task is composed of multiple interdependent subtasks. To bridge the gap, we formulate the problem of offloading multi-dependent tasks in multi-access edge computing considering both task completion time and execution cost. Since this offloading problem is NP-hard, a queue-based improved multi-objective particle swarm optimization is proposed. During the optimization process, we introduce the Pareto optimal relationship and define a transition probability to obtain the optimal solution. A large number of simulation results show that compared with other alternatives, the performance of our algorithm can be improved by about 3%–25%.