In view of the enormous potential of fluorescence chemosensors in recent years, more and more people focus on their developments. In the present work, we theoretically investigate a novel fluorescence sensor 2-{[2-(2-Hydroxy-phenyl)-1H-benzoimidazo-5-yl]-phenyl-methylene}-malononitrile (HBPMM) [J. Lumin. 2016, 173, 165] about its excited state intramolecular proton transfer (ESIPT) and probe response mechanism. Based on density functional theory (DFT) and time-dependent density functional theory (TDDFT) methods, we focus on the $S_0$-state and $S_1$-state hydrogen bonds dynamical behaviors and confirm that the strengthening intramolecular hydrogen bond in the $S_1$ state may promote the ESIPT reaction. In view of the photoexcitation, we find that the charge redistribution around hydroxyl moiety plays important roles in providing driving force for ESIPT. And the constructed potential energy curves further verify the ESIPT process of HBPMM should be ultrafast. That is the reason why the normal HBPMM fluorescence cannot be detected in previous experiment. Further, with the addition of fluoride anions, the exothermal deprotonation process occurs spontaneously along with the intermolecular hydrogen bond O-H•••F. It reveals the uniqueness of detecting fluoride anion using HBPMM molecule. As a whole, the fluoride anion inhibits the initial ESIPT process of HBPMM, which results in different fluorescence behaviors. This work presents the clear ESIPT process and fluoride anion sensing mechanism for the novel HBPMM chemosensor.