In this paper, center frequency down slift of ultrasonic echo signals which for the measurements of frequency dependent attenuation in the biological tissue are estimated. Center frequency down shift of echo-signals are estimated after signal spectrum analysis of whole echo-signals. In case of signal spectrums are simple, estimation of down shift frequency is very simple and in case of complicate spectrum, estimation of down shift frequency is depend on spectral shape. In case of unable to estimate, frequency dependence of medium is nonlinear(n) 1), in which upper shift of spectrums are presented. In case of unable to estimate, spectrum analysis are performed at local position. At consquence, we know that spectral dispersions are caused complicately by biological tissue layer.