In this paper, a new mathematical model for the entomopathogenic nematode with the Monod growth rate is formulated. Firstly, continuous release of the entomopathogenic nematode is considered. The existence of limit cycles, the Hopf bifurcation and the stability of the periodic solution created by the bifurcation are proved. The sufficient conditions for the globally asymptotical stability of system are obtained. Secondly, impulsive release of the entomopathogenic nematode is also considered. By using the Floquet’s theorem and the small amplitude perturbations, we show that the pest-free periodic solution is locally stable if some conditions are satisfied. In a certain limiting case, it is shown that a nontrivial periodic solution emerges via a supercritical bifurcation. Finally, our findings are confirmed by means of numerical simulations. Thus, we provide mathematical evidence on how to release the entomopathogenic nematode in order to control pests at acceptably low levels.