We demonstrate up-conversion single-photon detection for the 1550-nm telecommunications band using a PPLN waveguide, long-wavelength pump, and narrowband filtering using a volume Bragg grating. We achieve total-system detection efficiency of around 30% with noise at the dark-count level of a Silicon APD. Based on the new detector, a single-pixel up-conversion infrared spectrometer with a noise equivalent power of -142 dBm Hz(-1/2) was demonstrated, which was as good as a liquid nitrogen cooled CCD camera.