At present, the identification of toxic gases by electronic noses has a small amount of data, and the ability of neural network mapping generated by training is insufficient. In this work, the formaldehyde and methanol are used as target gases, and collected by self-made gas sensor. After filtering and smoothing the collected data, the different response values are extracted. The pseudo-random numbers are generated according to the criterion function, and the pseudo-random matrix is established to expand the effective data volume.The principal component analysis (PCA) is used to reduce the dimensionality of the eigenvalues, and the principal component score with large contribution rate is selected as the input vector of the back-propagation (BP) neural network to construct PCA-BP neural network, which is trained by using the measured eigenvalue matrix and the pseudo-random eigenvalue matrix respectively. By comparing the two networks, the recognition rate of the measured eigenvalue matrix is 92%, and the recognition rate of the pseudo-random eigenvalue matrix is 97%. The results show that the pseudo-random eigenvalue matrix can effectively improve the mapping ability of BP neural network and the accuracy of recognition.