We present in this paper analyses of the ROSAT PSPC and ASCA SIS and GIS observations of the Crab-like supernova remnant ( SNR ) G54.1+0.3 . Its spectrum obtained by ROSAT PSPC favors a power law model with a photon index of -0.8 ^ { +0.8 } _ { -2.0 } , absorbed energy flux in 0.1-2.4 keV of 1.0 \times 10 ^ { -12 } erg cm ^ { -2 } s ^ { -1 } , and absorption column density of 12.3 ^ { +8.0 } _ { -3.2 } \times 10 ^ { 21 } cm ^ { -2 } . ASCA SIS observation shows that its spectrum can also be best fitted with power law model . The fitted parameters are , photon index -1.9 ^ { +0.1 } _ { -0.2 } , absorbed energy flux in 0.7-2.1 keV 6.5 \times 10 ^ { -13 } erg cm ^ { -2 } s ^ { -1 } , and column density 17.9 ^ { +2.8 } _ { -2.5 } \times 10 ^ { 21 } cm ^ { -2 } . The high absorption column density indicates a distance similar to the radius of the galaxy . The 0.1-2.4 keV X-ray luminosity of G54.1+0.3 is 3.2 \times 10 ^ { 33 } d _ { 10 } ^ { 2 } erg s ^ { -1 } , where d _ { 10 } is the distance in 10 kpc . With an image restoration method we have obtained high spatial resolution X-ray image of the remnant , which clearly shows an X-ray jet pointing to the northeast with a length about 40 \arcsec from the center of the nebula . Its X-ray luminosity in 0.1-2.4 keV is about 5.1 \times 10 ^ { 32 } d _ { 10 } ^ { 2 } erg s ^ { -1 } . The X-ray jet is consistent with the radio extension to the northeast in both direction and position . We propose that the X-ray jet is connected with the pulsar assumed to exist in the remnant .