In Drosophila, olfactory information received by olfactory receptor neurons (ORNs) is first processed by an incoherent feed forward neural circuit in the antennal lobe (AL) that consists of ORNs (input), inhibitory local neurons (LNs), and projection neurons (PNs). This “early” olfactory information processing has two important characteristics. First, response of a PN to its cognate ORN is normalized by the overall activity of other ORNs, a phenomenon termed “divisive normalization.” Second, PNs respond strongly to the onset of ORN activities, but they adapt to prolonged or continuously varying inputs. Despite the importance of these characteristics for learning and memory, their underlying mechanisms are not fully understood. Here, we develop a circuit model for describing the ORN-LN-PN dynamics by including key neuron-neuron interactions such as short-term plasticity (STP) and presynaptic inhibition (PI). By fitting our model to experimental data quantitatively, we show that a strong STP balanced between short-term facilitation (STF) and short-term depression (STD) is responsible for the observed nonlinear divisive normalization in Drosophila. Our circuit model suggests that either STP or PI alone can lead to adaptive response. However, by comparing our model results with experimental data, we find that both STP and PI work together to achieve a strong and robust adaptive response. Our model not only helps reveal the mechanisms underlying two main characteristics of the early olfactory process, it can also be used to predict PN responses to arbitrary time-dependent signals and to infer microscopic properties of the circuit (such as the strengths of STF and STD) from the measured input-output relation. Our circuit model may be useful for understanding the role of STP in other sensory systems.