Due to the complexity of real environments, it is hard to detect toxic and harmful gases by sensors. To address such an issue, an artificial olfactory system is promoted, emulating the function of the human nose by means of gas sensors and an inference system. In this work, an artificial olfactory inference system based on memristive devices is developed to classify four gases (ethanol, methane, ethylene, and carbon monoxide) with 10 different concentrations. First, the spike trains converted from signals of the sensor array are inputted to a reservoir computing (RC) system based on volatile memristive devices, which extracts spatiotemporal features; then the features are processed by a classifier based on nonvolatile memristive devices; the output of the classifier indicates the classification result. Moreover, to reduce the device number and the power consumption, three strategies are applied to reduce the extracted features from the RC system. Eventually, the olfactory inference system successfully identifies the gases with a high accuracy of 95%.