We report here on the first pointed X-ray observation of the supernova remnant ( SNR ) G330.2+1.0 . The X-ray morphology is characterized by an extended shell . Its X-ray spectrum is well represented by a single power-law function with a photon index of \gamma \simeq 2.8 and interstellar absorption of n _ { H } \simeq 2.6 \times 10 ^ { 22 } [ cm ^ { -2 } ] . We interpret this emission as synchrotron radiation from accelerated electrons at the SNR shock , as seen in SN 1006 . The surface brightness of the X-ray emission is anti-correlated with the radio emission , and the power-law spectrum is dominated at the western shell where the radio emission is weak . The co-existence of two distinct ( radio bright/X-ray faint and radio faint/X-ray bright ) shells in a single supernova remnant challenges our understanding of the particle acceleration and radiation mechanisms in different interstellar environments . The object may be a good target for searching TeV gamma-rays and molecular gas surrounding the blast shock . We also report on the nature of a bright point-like source ( AX J1601 - 5143 ) to the south of the SNR .