  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, $S_{0.1r_{200}} = 143.9 \pm 18.3$ 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.
