To obtain fundamental data for the research of the transmutation of nuclear waste, the thermal neutron cross section of the reaction Sr-90(n,gamma)Sr-91 has been measured by means of a radiochemical method. Strontium chloride targets containing about 2MBq of Sr-90 were irradiated for 10 min with reactor neutrons. Activation detectors of Co/Al and Au/Al alloy wires were irradiated simultaneously to monitor the neutron flux and Westcott's epithermal index r(T/T0)1/2. The irradiated Sr samples were purified chemically and their gamma-ray spectra were measured with a high purity Ge detector. Since the targets included Sr-85, a gamma-ray emitter and a tracer for Sr-90, and a ratio of the amount of Sr-85 to that of Sr-90 was measured in advance, an effective cross section of the Sr-90(n,gamma)Sr-91 reaction for a reactor neutron spectrum was determined from the ratio of radioactivities of Sr-91 and Sr-85, and neutron flux data. The resonance integral was also measured by a modified Cd-ratio measurement. Considering an upper limit of the resonance integral to be 0.16b, the thermal neutron cross section (2,200 m/s neutron cross section) of Sr-90(n,gamma)Sr-91 reaction was found to be 0.0153 +/- 0.0013/0.0042 b. The value obtained is only 1/50 of the value reported by Zeisel (1966), and is in good agreement with the figure reported by McVey et al. (1983).