We report a measurement of the proton-antiproton total cross section sigma_T at c.m.s. energies s**(1/2) = 546 and 1800 GeV. Using the luminosity-independent method, we find sigma_T = 61.26 +/- 0.93 mb at s**(1/2) = 546 GeV and 80.03 +/- 2.24 mb at s**(1/2) = 1800 GeV. In this energy range, the ratio sigma_el/sigma_T increases from 0.210 +/- 0.002 to 0.246 +/- 0.004.