Host-parasitoid systems have proved fruitful models for many experimental and theoretical investigations in ecology and there is a rich literature on parasitoid population dynamics. Host-parasitoid systems have been modelled within a discrete-time framework. We can see discrete-time models can provide more efficient computational models for numerical simulations and these results reveal richer dynamics of the discrete models compared to the continuous ones. Interactions between plants and herbivores have been studied by ecologists for many decades.Even in simple one-species models, we have seen the potential for stability, cycles or chaos. One of the earliest applications of a discrete-time model to a biological system involved two insects, a parasitoid and its host. The model was developed by Nicholson and Bailey and applied it to the parasitoid, Encarsia formosa, and the host Trialeurodes vaporarioum (1935). In this thesis, we first define the concept of dynamical system and it’s component and we imply three important theorems of it, such as stability, bifurcation and chaos theory. These theorem have many applications on biological models and many researchers use them. They are also the base of my work. at this thesis. In section 3, we consider a simple host-parasitoid type model. The equilibrium solutions of this model are found. we investigate the type of bifurcations such as saddle-node, transcritical, pitchfork, period-doubling and the Neimark-Sacker bifurcations. Without the parasit, dynamics of this model is similar to the dynamics is given by the Ricker curve, such as period-doubling bifurcation, periodic windows and chaos. In section 4, we compare two general discrete-time host-parasitoid models with Allee effects on the host. In the first model, it is assumed that parasitism occurs prior to density dependence while in the second model, we assume that density dependence operates first followed by parasitism. It is shown that both models have similar asymptotic behavior. In section 5, we study the stability of models that using the work of Nicholson and Baily. Phase portraits are drawn for different ranges of parameters. Stable and oscillatory coexistence of host and parasitoid are observed.