In this work , we present a high spatial resolution study of a fossil cluster , SDSS J0150-1005 ( z \simeq 0.364 ) , based on the imaging spectroscopic analysis of Chandra observation . The Chandra X-ray image shows a relax and symmetric morphology , which indicates SDSS J0150-1005 is a well-developed galaxy cluster with no sign of recent merger . Its global gas temperature is 5.73 \pm 0.80 keV , and the virial mass is 6.23 \pm 1.34 \times 10 ^ { 14 } M _ { \odot } according to the isothermal model . Compared with polytropic temperature model , the mass calculated based on isothermal model overestimates 49 \pm 11 % . The central gas entropy , S _ { 0.1 r _ { 200 } } = 143.9 \pm 18.3 keV cm ^ { 2 } , is significantly lower than average value of the normal galaxy clusters with similar temperatures . Our results indicate the early formation epoch of SDSS J0150-1005 .