In fault diagnosis research, compound faults are often regarded as an isolated fault mode, while the association between compound faults and single faults is ignored, resulting in the inability to make accurate and effective diagnoses of compound faults in the absence of compound fault training data. In an examination of the rotate vector (RV) reducer, a core component of industrial robots, this paper proposes a compound fault identification method that is based on an improved convolutional capsule network for compound fault diagnosis of RV reducers. First, one-dimensional convolutional neural networks are used as feature learners to deeply mine the feature information of a single fault from a one-dimensional time-domain signal. Then, a capsule network with a two-layer stack structure is designed and a dynamic routing algorithm is used to decouple and identify the single fault characteristics for compound faults to undertake the diagnosis of compound faults of RV reducers. The proposed method is verified on the RV reducer fault simulation experimental bench, the experimental results show that the method can not only diagnose a single fault, but it is also possible to diagnose the compound fault that is composed of two types of single faults through the learning of two types of single faults of the RV reducer when the training data of the compound faults of the RV reducer are missing. At the same time, the proposed method is used for compound fault diagnosis of bearings, and the experimental results confirm its applicability.