Machine learning models have achieved remarkable success in intelligent fault diagnosis, but are mainly applied in static environments. In practical scenarios, new fault category data arrives continuously in the form of streams, and the distribution of the data changes due to changes in the operating conditions of the machinery and equipment, resulting in a continuous stream of data characterized by non-independent homogeneous distribution. This diagnostic problem of non-independently and identically distributed continuous stream data is called the continuous transfer diagnostic problem. To solve this problem, a continuous transfer learning system (CTLS) fault diagnosis method is proposed. The method includes a domain-adaptive learning loss function and a continuous transfer learning mechanism, which can efficiently handle industrial streaming data and learn new categories without replaying old category data. Moreover, a mechanical failure case evaluations validate the performance of the method, and analysis results show that CTLS can effectively handle industrial streaming data under different working conditions and is a promising tool for solving real industrial problems.