The advent of the intelligent society leads to the exponential growth of information, imposing urgent requirements in a time‐ and energy‐efficient way to process information where data are generated. This issue can be addressed by the neuromorphic paradigm of computing inspired by biological sensory systems that build up the association between external stimuli and the response of an organism in real‐time; in the paradigm, a neuromorphic system is integrated with sensors to form an artificial sensory system. Herein, a neuromorphic sensory system with integrated capabilities of gas sensing, data storage, and processing is demonstrated. Leaky integrate‐and‐fire (LIF) neurons, the basic computing units in the system, are realized with volatile memristive device Pt/Ag/TaOx/Pt; sensory neurons, i.e., the LIF neurons connected with an array of gas sensors, detect gases and convert the chemical information of gases into neural spikes; synapses based on nonvolatile memristive device Pt/Ta/TaOx/Pt transmit the signals from sensory neurons to relay neurons according to synaptic weights, which are trained by the supervised spike‐rate dependent plasticity; relay neurons then process the signals from the synapses and classify gases. The approach of this work can also be applied to emulate other biological perceptions through the integration with different sensors.