Particle Swarm Optimization has been an appealing research area for researchers for over 15 years. During these years, a variety of algorithms have been developed around the particle swarm concept. One of these variations is Predator-Prey Particle Swarm Optimization algorithm which is also based on natural swarms which have a hierarchical relationship. Hunting search has also become a new meta-heuristic originating from hunting structure of species. In this paper, a new Particle Swarm Optimization Algorithm has been developed. Animal Food Chain Based Particle Swarm Optimization Algorithm simulates the animal food chain structure in three swarms: omnivores, carnivores and herbivores, in order to balance exploration and exploitation.