This paper proposes a novel anomaly detection method for gas sensors using spiking neural network principles. The synapse models with excitatory/inhibitory responses and a single spiking neuron are employed to develop the bio-inspired anomaly detector for a single gas sensor. The approach can detect anomalies in the data, which is collected by the gas sensor by identifying rapid changes rather than a magnitude threshold. In particular, the false-positive detections due to the drifts of low-cost sensors are minimised using the proposed bio-inspired approach. Using the chemicals of surgical spirits and isobutanol as test substances, experiments were carried out to evaluate the proposed method. Results demonstrate that gas anomalies can be detected when the chemical substances are presented to the sensor. In addition, results show that the approach can detect under the presence of sensor drift. The proposed bio-inspired detector was implemented on FPGA hardware, which demonstrates relatively low resources. Compact and energy efficient CMOS-based implementations of the synapse are also available which supports the low-cost potential applications of this approach, e.g. use in safety with drones and ground robots in hazardous scene detection.