In this paper, we consider the optimal harvesting control of a biological species system whose growth is governed by the Gompertz equation with periodic
coefficients. The species is harvested at fixed moments for economic profit. The purpose is to control the harvesting effort so as to maximize the profit which
is the difference between economic revenue and cost, assuming that the cost in the payoff functional depends linearly on the control variable. The existence of an optimal impulsive harvest control is proven, and by the maximum principle for optimal impulse control  problem, and the optimal control is characteriged by using the optimality system. Two special cases are considered, and the  precise optimal controls are achieved for the two cases.