The acceleration mechanism of EUV/X-ray jets is still unclear. For the most part, there are two candidates for the mechanism. One is magnetic reconnection, and the other is chromospheric evaporation. We observed a relatively compact X-ray jet that occurred between 10:50 -11:10 UT on February 18, 2011 by using the Solar Dynamics Observatory/Atmospheric Imaging Assembly, and the X-ray Telescope, Solar Optical Telescope, and EUV Imaging Spectrometer aboard Hinode. Our results are as follows: 1) The EUV and X-ray observations show the general characteristics of X-ray jets, such as an arch structure straddling a polarity inversion line, a jet bright point shown at one side of the arch leg, and a spire above the arch. 2) The multi-wavelength observations and Ca II H-band image show the existence of a low-temperature (∼ 10 000K) plasma (i.e., filament) at the center of the jet. 3) In the magnetogram and Ca II H-band image, the filament exists over the polarity inversion line and arch structure is also straddling it. In addition, magnetic cancellation occurs around the jet a few hours before and after the jet is observed. 4) The temperature distribution of the accelerated plasma, which was estimated from Doppler velocity maps, the calculated differential emission measure, and synthetic spectra show that there is no clear dependence between the plasma velocity and its temperature. For the third result above, observational results suggest that magnetic cancellation is probably related to the occurrence of the jet and filament formation. This result suggests that the trigger of the jet is magnetic cancellation rather than an emerging magnetic arch flux. The fourth result indicates that acceleration of the plasma accompanied by an X-ray jet seems to be caused by magnetic reconnection rather than chromospheric evaporation.