Durations of gamma-ray bursts (GRBs) are featured by ＞2s subset and ＜2s one, with initial corresponding energy ratio being 20:1. It is found that supeova remants(SNR s) tuover frequencies peak at 100 and 500 MHz.After assuming that GRBs originate from hypeova and making an analysis on the evolution of GRBs, we find that the initial energy of two GRB subsets leads to a different radio-frequency tuover of their remnant spectra,which accords positively with the tuover-frequency ratio of SNRs.