The simplification of data processing is the frontier domain for electronic nose (e-nose) applications, whereas there are a lot of manual operations in a traditional processing procedure. To solve this problem, we propose a novel data processing method using the bio-inspired neural network modeled on the mammalian olfactory system. Through a neural coding scheme with multiple squared cosine receptive fields, continuous sensor data are simplified as the spike pattern in virtual receptor units. The biologically plausible olfactory bulb, which mimics the structure and function of main olfactory pathways, is designed to refine the olfactory information embedded in the encoded spikes. As a simplified presentation of cortical function, the bionic olfactory cortex is established to further analyze olfactory bulb's outputs and perform classification. The proposed method can automatically learn features without tedious steps such as denoising, feature extraction and reduction, which significantly simplifies the processing procedure for e-noses. To validate algorithm performance, comparison studies were performed for seven kinds of Chinese liquors using the proposed method and traditional data processing methods. The experimental results show that squared cosine receptive fields and the olfactory bulb model are crucial for improving classification performance, and the proposed method has higher classification rates than traditional methods when the sensor quantity and type are changed.