In this work, we consider a nonlinear budworm model by a system of three ordinary differential equations originally created by Ludwig et al. in 1978. The nonlinear system describes the dynamics of the interaction between a budworm and a fir forest. We introduce stability techniques to analyze the dynamical behavior of this nonlinear system. Then we use constant effort harvesting techniques to control the budworm population. We also give numerical simulations of the population model with harvest and without harvest.