We proposed a linear type magnetic flux pump (LTMFP) as a power supply for superconducting magnet system. In order to explain the operating mechanism of pumping action, the pumping sequence based on penetrated position and moving speed of magnetic flux on the superconducting Nb foil should be understood. In this paper, we induced a theoretical equation for pumping current of LTMFP according to the position of normal spot and corresponding equivalent circuit. In addition, current charging tendencies under the intensity of magnetic flux and frequency were described based on the theoretical pumping equation.