Abstract: Firstly, the approximate formulas between lightning electromagnetic fields and return-stroke channel base current are derived in field range and far field range in this paper, after that we researched the effect of return-stroke speed on relationship between channel base current and lightning electromagnetic fields in near area and far area, respectively. Result show that，the difference between channel base current and lightning electromagnetic fields in near area is concentrated in the peak portion of waveforms, while the difference between channel base current and electromagnetic fields in far field range is focused on the falling edge part of waveforms, but the differences between them are decrease with the increase of return－stroke speed. If the return－stroke speed is equal to speed of light, the approximate equations between channel base current and lightning electromagnetic fields in near area and far area will normalized to unified expressions, which validated that if v=c electric and magnetic field waveforms and channel base current waveform are identical at all point in space.