In this paper, the fine-structures of lightning electromagnetic pulse (LEMP) including 19 pulses in preliminary breakdown, 37 stepped leaders, 8 dart leaders, 73 first return strokes, and 52 subsequent return strokes have been analyzed based on Laplace wavelet. The main characteristics of field waveforms are presented: the correlation coefficient, the dominant frequency, the peak energy and the spread distribution of the power spectrum. The instantaneous field peak pulse can be precisely located by the value of the correlation coefficient. The pulses of preliminary breakdown and leaders are found to radiate in the dominant frequency in the range 100 kHz to 1 MHz. The field radiated by the first return strokes dominantly lies under 100 kHz, whereas the subsequent return strokes under 50 kHz. The statistical results show that the Laplace wavelet is effective and can accurately determine time and frequency of the electromagnetic field of first and subsequent return strokes.