There are two drive modes for an active magnetic bearing (AMB), namely the current and voltage drive modes. The analytical model of an AMB is second-order under current drive and third-order under voltage drive. The current drive is widely used due to its simple model. However, it is not the case in a solid-core AMB since it is subject to strong eddy currents. System identification is adopted in this paper to obtain the accurate model of a solid-core AMB, which shows that a third-order model is required to describe the real system in both current and voltage drive modes. Under the influence of eddy currents, the order of the model is increased in the current drive mode, whereas is not in the voltage drive mode, indicating that the model in the voltage drive mode describes the system dynamics better. All the details of the solid-core AMB, identification method and experimental results are given in this paper. In addition, a new numerical algorithm is proposed to simplify the existing least square method, which needs no iteration, achieves similar accuracy and is not restricted to our application.