Pursuing prey by a predator is a natural phenomenon. This is an event when a predator targets and chases prey for consuming. The motive of a predator is to catch its prey whereas the motive of a prey is to escape from the predator. Earth has many predator species with different pursuing strategies. Some of them are sneaky again some of them are bolt. But their chases fail every time. A successful hunt depends on the strategy of pursuing one. Among all the predators, the Dragonflies, also known as natural drones, are considered the best predators because of their higher rate of successful hunting. If their strategy of pursuing a prey can be extracted for analysis and make an algorithm to apply on Unmanned arial vehicles, the success rate will be increased, and it will be more efficient than that of a dragonfly. We examine the pursuing strategy of a dragonfly using LSTM to predict the speed and distance between predator and prey. Also, The Kalman filter has been used to trace the trajectory of both Predator and Prey. We found that dragonflies follow distance maintenance strategy to pursue prey and try to keep its velocity constant to maintain the safe (mean) distance. This study can lead researchers to enhance the new and exciting algorithm which can be applied on Unmanned arial vehicles (UAV).