The collisional quenching of OH A 2-SIGMA-(upsilon' = 1) by H2O was determined from laser-induced fluorescence measurements in the burned-gas region of stoichiometric H-2/O2/Ar flames at low pressure (19 and 38 Torr). The collisional quenching was measured as a function of the initial laser-populated rotational level for N' = 4, 5, 8, 9, 10 and 11. The quenching cross section after laser excitation to N' = 4 is 32 +/- 2.5 angstrom 2 at a temperature of 1048 K, approximately 40% of its value at room temperature. The quenching cross section decreases by 17% as the initial laser-excited rotational level is increases from N' = 4 to N' = 11. This variation in quenching rate has a significant effect on the determination of OH rotational temperature from laser-excitation spectra. Accounting for the variation of quenching with rotational level reduces the rotational temperature by 10% at 1100 K. The collisional quenching cross section of OH A 2-SIGMA-(upsilon' = 1) by H atoms was calculated to be 10 +/- 3 angstrom 2 for N' = 5 at a temperature of 1048 K.