In this paper,we construct an oligopoly game of renewable resource extraction in which the growth rate is fixed at a constant and the unit production cost function takes the linear form. We study the equilibrium equation satisfied by the equilibrium strategy of the players,and discuss the long-run properties of the total resource reserve level and the total extraction rate on the equilibrium path of the game. The mathematical analysis shows that the extraction strategy which neglects the long-run profits will exhaust the resource at all in the long time and the one which emphasizes the long-run profits will make the resource grow hence get its sustainable development in the long run.