Establishing an anomaly detection model as quickly as possible with a small number of measurement samples for use with new equipment or working conditions has been a research focus. In recent years, despite the effectiveness of transfer learning techniques in terms of coping with such problems, it is still challenging to map the detection rules of an existing device to a target device to enhance its single-class anomaly detection capabilities. In addition, the robustness requirement of the detection rule transfer process makes the problem further complicated, particularly in cases where limited target device data still have unknown outliers. To achieve good anomaly detection performance in such a complex scenario, we propose a robust deep one-class support vector description-based anomaly detection algorithm built on adversarial transfer learning. First, we designed a new hyperspherical adversarial training mechanism that integrates robust adaptive constraints into an improved domain-adversarial neural network. Additionally, to eliminate outlier interference to the greatest extent possible during the domain-adversarial process, we aimed to compute the probability of a sample being normal based on the utilized anomaly detection module and embedded this probability in a domain discriminator. Finally, an end-to-end optimization strategy was derived to find the optimal network parameters that could separate the anomalous classes as much as possible while promoting the consistency of the normal class data in the source and target domains. To validate the performance of our model, we experimented with three scenarios, i.e., digit image detection (with the MNIST and USPS datasets), object recognition (with the Office-Home dataset), and rolling bearing anomaly detection. The results showed that the proposed algorithm outperformed the state-of-the-art methods in terms of detection accuracy and robustness.