Due to the properties of high temperature superconducting (HTS) materials, current attenuation is inevitable during the closed-loop operation of HTS magnets. When a contact DC power supply is used to supplement this attenuation, it inevitably creates a huge thermal burden on the cryogenic system. The flux pump is a revolutionary new power source that can charge closed-loop HTS magnet wirelessly. However, for HTS magnets with a large inductance, the flux pump cannot fast adjust the DC current of the magnet, due to its small DC output voltage. Here, we present a method to fast regulate the current in a closed-loop HTS magnet using a contact DC power supply and persistent current switch (PCS). After current regulation, the HTS magnet is operated in the persistent current mode (PCM) with a flux pump. By applying the “four-quadrant” control theory of the flux pump allows, the current in HTS magnet is controlled with  high stability. This study provide a power strategy for the fast current regulation and maintenance of persistent current in the HTS magnet, enabling the industrial applications of flux pumps for HTS magnets with large inductance.