A differential-algebraic model which discusses a prey-predator system with harvest effort on predator is proposed. By using the differential-algebraic system theory and bifurcation theory, local stability of the proposed model around the interior equilibrium is investigated. The instability mechanism of the proposed model due to the variation of economic interest of harvesting is studied. In order to stabilize the proposed model around the interior equilibrium and maintain the economic interest of harvesting at an ideal level, a state feedback controller is designed. Finally, numerical simulations are carried out to show the consistency with theoretical analysis.