The emission of a 41 THz quantum cascade laser (THz QCL) has been measured by a spectrally-matching terahertz quantum-well photodetector (THz QWP). The measured emission spectra have been analyzed with respect to the spectral shape and peak position. The relative light power of the laser under different drive currents have been estimated from the emission spectra and then the lasing domain and threshold current density of the laser has been determined. The temperature-dependent response of THz QWP to the laser has also been investigated. The analyzed results indicate that the THz QWPs could be a good detector for characterizing the emission properties of the THz QCLs and may be the receivers in the terahertz communications.