SO2 emissions are known to pose great harm to both human health and atmospheric air, and flue gas generated from coal-fueled power plant is the prime source of sulfur dioxide. For this reason, flue gas desulfurization (FGD) technology has found wide applications in most coal-fired power stations. Correctly describe the dynamic behavior of an FGD process is the precondition of controlling it effectively. However, FGD process modeling is by no means an easy task, as the underlying process dynamics are highly nonlinear in nature, meanwhile time-delay effect is significant therein. Long short-term memory (LSTM) network possesses remarkable long-term memory capability, hence it is anticipated to have a powerful identification capability. In this paper, the connection between deep learning and system identification is established, further a unidirectional/bidirectional LSTM deep network is designed and employed to identify a real FGD process. Simulation results clearly demonstrate the effectiveness of deep learning-based identification approach, and the superiority of deep LSTMs over other conventional identification models is also verified.