We perform a bifurcation analysis of a predator-prey model with Holling functional response. The analysis is carried out both analytically and numerically. We use dynamical toolbox MATCONT to perform numerical bifurcation analysis. Our bifurcation analysis of the model indicates that it exhibits numerous types of bifurcation phenomena, including fold, subcritical Hopf, cusp, Bogdanov-Takens. By starting from a Hopf bifurcation point, we approximate limit cycles which are obtained, step by step, using numerical continuation method and compute orbitally asymptotically stable periodic orbits.