In this paper, we aim to propose a new chemostat model with continuous microbial culture and harvest, and to investigate the dynamics of the model. Different to the conventional ones, our model includes a constant periodic flocculant transmission. For the proposed system, by using theory of impulsive differential equations, we show that the microbe-extinction periodic solution is globally asymptotically stable when a threshold value is less than 1, and system is permanent when a certain threshold value is greater than 1. Then, according to the threshold associated with microbial extinction or existence, the control strategy for microbial continuous cultivation and harvest is discussed. Under such control strategy, continuous microbial culture and harvest can be achieved by adjusting input time, input amount or concentration of the flocculant. Finally, an example with numerical simulations is given to illustrate our theoretical conclusions.