The present study proposes a quasi-static finite-difference time-domain (FDTD) method for dosimetry in humans due to contact current at low frequencies (10 kHz). Our attention focused on wave sources which can reduce computational time. The computational time was found to be reduced using a voltage source of a step function with smooth start. The computational time required for the proposed method was smaller than a quasi-static FDTD method proposed in a previous study. Comparison between our computational results and those in a previous study suggested the effectiveness of our proposal. The difference in in-situ electric field due to different human models was a factor of 2 or so.