In this paper the dynamics of the Lotka-Volterra predator-prey model subject to a variable structure control is studied applying bifurcation analysis techniques. This methodology allows to determine a complete characterization of the system dynamics when some selected control parameters are changed. The main contributions of the paper are: (i) an analysis of the effects of the harvesting policy for different combinations of the control parameters; (ii) the establishment of necessary and sufficient conditions in order to guarantee global stability of a desired equilibrium in predator-prey populations under harvesting action.