The electronic nose (e-nose) is a highly advanced detection technique with numerous practical uses in the areas of food, health, environment, and safety. Especially in certain hazardous situations and repetitive mechanical use, using portable and compact e-nose detection equipment can significantly minimize harm to individuals and economic costs. This requires the combination of advanced artificial intelligence algorithms and low-power hardware to design some low-power, miniaturized, and high-speed response e-nose devices. This article proposes a compact and low-power computing scheme with a memristor-based in-memory computation accelerator for the multi-gas sensor-processing system. We first created a platform for acquiring gas data and gas concentration from a multi-gas sensing array and processed it in 2-D to make it suitable for a convolutional neural network (CNN). A new 16-level nonvolatile ReRAM memory in-store computation scheme is used to achieve parallel multiplication and addition computations. A hybrid quantization accuracy-aware algorithm was also designed to improve the recognition accuracy of the neural network with low-bit quantization weights. When using 4-bit weight quantification, the identification accuracy of gas and gas combination concentration reached 95.2% and 94.67%, respectively. Finally, we deploy the trained network weights of each layer into the in-memory computation accelerator. Based on the ON-chip experimental results, our proposed in-memory computation acceleration scheme achieves impressive recognition accuracies of 94.69% and 94.21% for classifying ten different gases and identifying their concentrations, even when utilizing 4-bit quantized weights. Moreover, it takes less than 0.4 ms to perform a single inference with 20.2-mW power consumption. These results demonstrate that our work has great potential for applications in low-power, low-latency, and compact e-noses.