Abstract: The relationship between the pulse FWHM (full-widths at half maximum) and the energy of gammaray bursts (GRBs)is explored based on the observed data from BATSE data base (http//cossc gsfc nasa gov/atse/).Based on a sample of 64 FRED (fast rise and exponential decay)pulse bursts better fitted with the KRL model (refer equation (22)in 1), it is found that 63, out of the 64 sources, belong to either the platformpower-law-platform feature class or the peaked feature group.The classifications for 64 sources could be sorted into five models in detail a)a power law range could be observed in 34 sources;b)a lower band platform could be observed or suspected in 18 bursts;c)a higher band platform could be observed or suspected in 7 sources;d)a peaked feature could be observed or suspected in 4 GRBs;e)the other model from the four types above could be observed in 1 sources.The result suggests that there exists a power law relationship between the pulse FWHM of GRBs and the energy.And the result confirms the points from Qin et al (2005)2 that the relationship is due to the Doppler effect of fireballs.