The total neutron cross sections of 235U, 238U, and 239Pu were measured over the energy range 0.5 to 15 MeV, using the U.S. National Bureau of Standards electron linear accelerator as a pulsed neutron source. Neutron energies were measured by the time-of-flight method, with a resolution of 0.1 nsec/m. The measurement accuracy is estimated to be ±1%. The cross-section curve is smooth, with no observable fine structure. The data are in excellent agreement with recent results from the Rensselaer Polytechnic Institute, and in satisfactory agreement with the ENDF/B-III data file, except at the high and low energy ends of our energy range.