The olfactory system in insects has evolved to process the dynamic changes in the concentration of food odors or sex pheromones to localize the nutrients or conspecific mating partners. Experimental studies have suggested that projection neurons (PNs) in insects encode not only the stimulus intensity but also its rate-of-change (input gradient). In this study, we aim to develop a simple computational model for a PN to understand the mechanism underlying the coding of the rate-of-change information. We show that the spike frequency adaptation is a potential key mechanism for reproducing the phasic response pattern of the PN in Drosophila. We also demonstrate that this adaptation mechanism enables the PN to encode the rate-of-change of the input firing rate. Finally, our model predicts that the PN exhibits the intensity-invariant response for the pulse and ramp odor stimulus. These results suggest that the developed model is useful for investigating the coding principle underlying olfactory information processing in insects.