A multivariate process fault diagnosis model is proposed based on convolutional neural network (CNN), aiming at extracting effective features from complex multivariate processes and improving fault diagnosis performance. First, the high-dimensional process signals are normalized and then converted into images. Second, a lightweight CNN network composing of multi-layer convolution filters and sub-sampling filters is convolved with images through multiple convolution kernels, using local connections and shared weights to remove noise and interference information to obtain the high-level abstract representations of process data. Finally, a Softmax layer is used in a supervised way to implement fault diagnosis. Tennessee Eastman Process is used to verify the effectiveness of proposed model and compare the performance between the proposed model with classical classifiers and deep neural networks. The results show that the fault diagnosis accuracy is improved by converting high-dimensional process signals into images. The t-SNE visualization analysis method is used to illustrate the powerful feature extraction ability of proposed model. The features extracted by the proposed model are sent to the traditional classifiers and the accuracy of fault identification is significantly improved, which further illustrates the benefit of effective feature extraction for improving the fault diagnosis accuracy and reliability. Compared to unsupervised learning, the proposed model with the guidance of label helps to extract more efficient, stable, and abstract feature representations.