To detect the terahertz radiation of a low temperature blackbody accurately, the difference between infrared radiation and different terahertz radiations of the blackbody was researched. A low temperature blackbody terahertz radiometer was established with narrowband spectral filtering method. First, the emitted spectral radiances were calculated by Planck′s law in various terahertz wave bands. The results show that the radiances of blackbody in the infrared band are four to ten times than that in the terahertz band from 223 K to 323 K. Then a low-pass filter and several band-pass filters were made up a filter combination with high transmission in various wavelengths. The filter combination was used to filter the infrared radiation and to transmit the terahertz radiation to implement the terahertz spectral radiance measurement. Experimental results reveal the deviations of terahertz narrowband radiations at different bands for the blackbody and indicate that spectral filtering method can realize the detection of terahertz radiation of the blackbody.