AC circuit breaker's controlled switching is a popular method to reduce dielectric and thermal stresses during switching of transformers, transmission lines, reactor and shunt capacitors. The magnitude of inrush current often reaches five to nine times of rated magnetizing current and thus it affects the network stability. Particularly, it affects the superconductivity of HTS transformer. Moreover, a residual flux is developed in HTS transformer due to high inrush current. The amount of flux may increase to a very high value that has direct impact to have a very high transient inrush current. This paper presents inrush current mitigation phenomena in a single-phase HTS transformer by controlled switching of HTS breaker arc model. The inrush current phenomenon is modeled for a single-phase HTS transformer in this paper. The mitigation of inrush current is restrained to a lower level by the reclosing of a new type of arc model named HTS breaker arc model and the residual flux also minimized. The calculating method is established on the investigation of fast switching timing and characteristics of the HTS breaker arc model.