Drones or Unmanned Aerial Vehicles (UAV) have recently become popular, especially in civilian and military applications. Examples of drone utilization are reconnaissance mission, packet delivery system, and surveillance system. As the technology grows to be more advanced, drone’s tasks become more complex and they need more computation power. Hence, clusters or swarms of drones are preferred since the swarms can offer more flexibility, reliability, and coverage. One weak point of drones is their limited computing and energy resources; therefore, it is hard for drones to process all the application on time. One possible solution to mitigate the problem is by doing offloading scheme between drone clusters. In this study, we proposed an opportunistic computation offloading system, which permits swarm drones with high computation applications to opportunistically borrow neighbor drone cluster’s available computation resources. Furthermore, we designed a response time estimation module by adopting artificial neural network technique in order to decide whether it is faster to complete the jobs by offloading the tasks to the nearby drone clusters or not. The offloading process will be only done if the estimated offloading scheme’s response time is smaller than the response time of executing the tasks locally. Our simulation results show that the proposed scheme can decrease the application response time by conducting opportunistic offloading process.