The increasing demand for diversified and large-scale computing poses a huge challenge to the real-time computing capabilities of edge servers (ES) in distribution networks. Collaborative computing through different edge servers is an effective solution. To address this issue, a task offloading strategy based on Stackelberg game under edge edge collaborative computing was proposed, to improve computational efficiency and the benefits of edge servers. Based on the task-level cooperative computation model established for the distribution grid, a task offloading model based on Stackelberg game was established with the goal of achieving optimal overall performance in terms of task execution delay and computation cost. Furthermore, the existence of Nash equilibrium was proven and its solution method was provided. Finally, a cooperative task offloading method for edge-edge in distribution networks based on the Stackelberg game was designed. The case study results show that in terms of task execution utility value, the proposed method improves by 35.8% and 48.4% compared to the common greedy offloading method and the random offloading method, respectively. In terms of task execution latency, the proposed method improves by 19.8% and 32.9% compared to the random offloading method and local execution, respectively.