Developing fault diagnosis for the cooling dehumidifier is very important for improving the equipment reliability and saving energy consumption. This paper mainly studies and explores the compound fault diagnosis for the cooling dehumidifier. Firstly, the dehumidifier data acquisition system is built, which can be applied to the data acquisition, work status simulation, and fault diagnosis. Secondly, a compound fault diagnosis model based on radial basis function neural network (RBFNN) improved by kernel principle component analysis (KPCA) and adaptive genetic algorithm (AGA) is proposed. Aiming at the problems that the selection of RBF width depends on expert knowledge, the network structure scale is large or the training speed is slow in the conventional RBFNN models, on the one hand, AGA and K-means clustering algorithm are employed to automatically optimize the RBF width, the number of hidden layer neurons and the neuron centers, which guarantees the model has small structure and fast computing speed on the premise of sufficient output precision; on the other hand, KPCA is used to reduce the dimension of the model input data, which not only effectively extracts the nonlinear features, but also further simplifies the network structure. Finally, the proposed method is validated and compared with the conventional models. The results show that this proposed model can not only be effectively applied to the dehumidifier compound fault diagnosis, but also has prominent application advantages.