Seismic envelope of coda waves is an efficient measure to estimate physical parameters of the Earth heterogeneity. For NS component seismograms of regional earthquakes recorded by 11 IRIS stations, applying the Hilbert transform to make seismic envelopes in period bands from 0.25--0.5s to 16--32s with lapse time as long as 4000s, we discovered that coda envelopes decay according to some power of lapse time measured from the origin time. It is new and different from the present knowledge about coda envelopes which have been described by several bending curves with different decay rates. The 'power-law' decay characteristic of seismic envelopes indicates that the spectra amplitude of seismic coda could be simply expressed as of the form A(t,TC) $propto$ t-α(TC), where t is lapse time and TC is central period in second. Applying regression analysis, we found that the exponent α value has period dependence and ranges α1 = 1.3~6.5 (0.25--0.5s~16--32s), α2 = 0.6~6.1 (0.5--1s~16--32s) for before and after ScS arrival, respectively. Moreover, it shows no significant difference between shallow and deep focus events for periods shorter than 8s. The simple and distinct characteristics of seismic coda envelopes could provide reliable information to determine physical characteristics such as attenuation and scattering to identify the regional difference of medium heterogeneity in the Earth.