In order to understand how olfactory stimuli are encoded and processed in the brain, it is important to build a computational model for olfactory receptor neurons (ORNs). Here, we present a simple and reliable mathematical model of a moth ORN generating spikes. The model incorporates a simplified description of the chemical kinetics leading to olfactory receptor activation and action potential generation. We show that an adaptive spike threshold regulated by prior spike history is an effective mechanism for reproducing the typical phasic–tonic time course of ORN responses. Our model reproduces the response dynamics of individual neurons to a fluctuating stimulus that approximates odorant fluctuations in nature. The parameters of the spike threshold are essential for reproducing the response heterogeneity in ORNs. The model provides a valuable tool for efficient simulations of olfactory circuits.