Two new methods for estimating spatial distribution of acoustic attenuation coefficient in biological tissue using the ultrasonic echo short-term spectral moment analysis are proposed and discussed. Short-term spectral moments are calculated from the autocorrelation function of analytic signal and its derivatives. Experimental results on the dextran particle suspension in condensed milk are also presented. In one method, the slope of attenuation coefficient vs. frequency is calculated from the 1-st order normalized moment differentiated and divided by 2-nd order normalized moment around centroid frequency. In the other method, the slope is calculated from the O-th order unnormalized moment differentiated and divided by 1-st order unnormalized moment differentiated and divided by 1-st order unnormalized moment around origin. The latter is considered to give the estimate with fairly low stochastic variation compared with the former because the latter uses lower order moments than the former does, and this is confirmed experimentally. Both method require the knowledge on frequency characteristics of sound field or that of scattering in the region of interest if the local spatial change of those characteristics is negligible. In near field, this spatial change cannot be neglected. The correction of this effect was performed using the spatially uniform scattering material, and the results were satisfactory. These results suggest that the realization of realtime attenuation tomography is promising.