Based on the data from the observation of the supernova remnant ( SNR ) G327.1-1.1 by Advanced Satellite for Cosmology and Astrophysics ( ASCA ) and ROSAT , we find that G327.1-1.1 is a composite remnant with both a nonthermal emission component and a diffuse thermal emission component . The nonthermal component is well fitted by a power-law model with photon index \Gamma \sim 2.2 . This component is attributed to the emission from the synchrotron nebula powered by an undiscovered central pulsar . The thermal component has a temperature of about 0.4 keV . We attribute it to the emission from the shock-heat swept-up ISM . Its age , explosion energy and density of ambient medium are derived from the observed thermal component . Some charactistics about the synchrotron nebula are also derived . We search for the pulsed signal , but has not found it . The soft X-ray ( 0.4 - 2 keV ) and hard X-ray ( 2 - 10 keV ) images are different , but they both elongate in the SE-NW direction . And this X-ray SE-NW elongation is in positional coincidence with the radio ridge in MOST 843MHz radio map . We present a possibility that the X-ray nonthermal emission mainly come from the trail produced by a quickly moving undiscoverd pulsar , and the long radio ridge is formed when the pulsar is moving out of the boundary of the plerionic structure .