A combination method using γ -ray and thermal neutron detectors was newly applied to the accurate evaluation of power histories during reactivity-initiated power burst experiments in the Transient Experiment Critical Facility (TRACY). During an initial power burst, the power history was determined using a fast response γ -ray ionization chamber, which was used because of its ability to exactly trace the power history within a short duration of the initial burst. After the initial burst, a micro fission chamber containing highly enriched uranium was used for the determination of the power history because the γ -ray ionization chamber could not be applied due to the contribution of delayed γ rays from fission products. By the present method, the power histories were evaluated for the experiments in the range of 1.50 to 2.93$ of the reactivity insertion. It was found that the peak power and integrated power as determined by the previous method using only the micro fission chamber were underestimated to be 40% and 30% in maximum, respectively, in comparison with the results from the present evaluation. The numerical simulation performed by using the Monte Carlo method indicated that the underestimation could be comprehended by considering the time delay of thermal neutron detection of the fission chamber, which arose from the flight-time of neutrons from the TRACY core to the fission chamber.