Fault detection might effectively enhance the operational reliability and safety of industrial robot (IR). Data-driven intelligent detection methods are dependent on a certain number of fault samples. However, the fault samples of the IR are difficult to be obtained and even unavailable. To overcome the mentioned shortcomings, a newly residual shrinkage transformer relation network (RSTRN) is proposed in the paper for fault detection of the IR. In this method, a residual shrinkage network is applied to eliminate interference features hidden in the input signals and extract representative features. And, the feature sample pair is created to describe relationship between the health state and other states. Then, the transformer relation network is constructed to evaluate the similarity relations between the sample pair to determine their types. In addition, an auxiliary sample library is built to help the RSTRN in extracting more firm health features. Finally, the effectiveness of the RSTRN method is verified by using self-built IR experiments. The experimental results show that detection accuracy and recall of the RSTRN method is at least 25% higher than that of existing methods, and its noise immunity is also improved.