With the development of the high-temperature superconducting material, the high-temperature superconducting machine becomes the very important research direction in the electrical machine domain. It integrates the advantages of high-power density, small machine size, and zero resistance of the superconducting windings. In this paper, taking an axial-radial flux-type high-temperature superconducting permanent-magnet synchronous motor (ARFTHTSPMSM) as an example, based on the investigations about the configuration characteristics and the operation principles of such machine, the mathematical model for the 3-D transient electromagnetic field was established. The magnetic field in this motor was analyzed by using the time-stepping finite-element method. In addition, the distribution characteristics of the magnetic flux in the air gap and ferromagnetic bridge were discussed, and then, the variations of the air-gap flux density, ferromagnetic bridge flux density, and non-load back electromotive force were analyzed when the motor is operating at different axial magnetic motive force. Both the theoretical analysis results and the experimental data indicate the notable advantage of adjustable excitation in such machine. Finally, based on the aforementioned analysis, the rotor eddy current losses were calculated, and their distribution characteristics were studied when the motor is operating at the starting process and the steady state, respectively. The obtained conclusions may provide useful reference for the design and research on the ARFTHTSPMSM.