Abstract In this paper the following assumptions are made: (1) Prominences (filaments) or some of EUV and X-ray loops are probably the main current circuits in active regions. (2) The magnetic field in an active region is composed of the one activated by current circuits and the so-called background magnetic field. (3) The evolution of the magnetic field and current is closely related to matter motion in active regions. According to the Kuperus-Raadu model, we solved the momentum equation and the energy equation of the current circuits by the numerical method, in terms of several main forms of the observed matter motion in active regions. The regularities of evolution of the currents were obtained. These results expounded theoretically the intrinsic relation among the occurrence of flares, their main physical processes, the matter motion and the evolution of currents in active regions.