Prey-predator’s interaction are the most important relationship between populations. Prey-predator interaction depends on many different factors such as predator response, prey and predator behaviour, and many more. In this research, I’ll study the effect of prey and predator’s behaviour in the dynamics of prey-predator dynamics. To achieve this goal, two models, with one prey and two predators and prey refuge were developed and studied. One model assumes that there is no competition between these two predators, and the other one assumes that there is a competition between them. Our results show that the aggressiveness of the predator is not good for its existence in case of no competition between the two types of predators, and in the case of the competition the least aggressive predator goes to extinction.