We present a study of a jet observed by the Solar Dynamics Observatory (SDO) and the Interface Region Imaging Spectrograph (IRIS), which provide high spatial-temporal resolution observational data of (extreme) ultraviolet images, spectra, and magnetograms. The jet was observed in multiple bands of AIA and manifested clear bidirectional flows in IRIS observations. The emission profiles of the Si IV 1402 angstrom line of the jet exhibited non-Gaussian features and double-peaked spectra, with the Doppler velocity and the nonthermal velocity up to 100 and 160 km s-1, respectively. The plasma flows of the jet projected on the sky plane and in the line of sight (LOS) are the typical observational evidence of magnetic reconnection. The EM loci curves indicated that the plasma contains multi-temperature components. The result deduced from the DEM method and changes in intensity of several spectral lines imply that the temperature of the plasma in the jet is heated to at least 105.6 K. The electron density is about 1011 cm-3 according to the intensity ratios of the O IV 1399.77/1401.16 angstrom doublet and Si IV 1402.77/O IV 1401.16 angstrom lines. Via different approaches, we reached the conclusion that the jet occurred in the upper chromosphere. Investigating the magnetograms in the period when the jet appeared, we suggest that the jet results from the magnetic reconnection between the moving magnetic structure and the magnetic field nearby.