At the wavelength of 1064 nm, the absolute optical power responsivities of two Si trap detectors were measured against the cryogenic radiometer. The calibration method and experiment equipment were discussed, as well as analysis of the measurement data. A new quasi in-situ measurement scheme of Brewster windows transmittance was proposed and transmittance higher than 0.999 was obtained. Results show that the combined uncertainties of the responsivity are1.457×10ˉ4 and 1.458×10ˉ4, and the measurement repeatabilities of the two trap detectors were within 0.014% and 0.008%, respectively. The uncertainties and possible error sources during the process of measurement were analyzed and evaluated. The temperature stability of optical power responsivity of 0＃ trap detector was studied at the wavelength of 1064 nm.