Chemical production usually shows complex, higher-dimensional, time-varying, and non-Gaussian characteristics, which make it difficult to judge the normal operation of the states of chemical processes. The various and similar fault states in chemical processes cause difficulties to existing fault diagnosis methods. In order to solve this problem, a feature fusion fault diagnosis method using a normalized convolutional neural network for complex chemical processes is proposed in this paper, which consists of the depth-normalized convolution network, improved second-order pooling, and multilayer perceptron. First, the original data that have been simply processed are put into the depth-normalized convolution network to extract features of the faulty states. Second, the output of depth convolution modules enters into the improved second-order pooling to proceed feature fusion for further refining the state characteristics. Finally, the multilayer perceptron is used to extract and compress the following features, and the final diagnosis results are obtained. In this paper, the normalized convolution network model is established by adding the batch normalization into a one-dimensional convolution network, where the problems of gradient explosion and disappearance are partly avoided. Meanwhile, the convergence speed of the network is also accelerated. The experimental tests on a Tennessee Eastman process and a coking furnace process show that the proposed method is more advanced than existing deep learning fault diagnosis methods.