The instability behavior of a viscoelastic plane liquid sheet in compressible invisicid ambient gas is investigated in the present study. Non-dimensionalized plots of the solutions exhibit the stabilizing or destabilizing influences of various parameters on the liquid sheet. Both spatiotemporal analysis and temporal instability analysis were conducted. The results show that larger Weber number can promote the flow to be convectively unstable. The increase of Reynolds number can decrease the absolute growth rate. The variations of Mach number and elasticity number rarely change the spatial-temporal behavior of the plane sheet when the flow is absolutely unstable. For the temporal mode, when the liquid Weber number is small enough, with the increase of Reynolds number or elasticity number, the maximum growth rate becomes smaller. With a larger Weber number, the increase of Reynolds number or elasticity number can enlarge the maximum growth rate. In addition, it has been found that with the increase of Mach number, the growth rate first decreases and then increases when We = 3; when We = 500, the increase of Mach number can enlarge the growth rate. Note that high Weber number will accelerate the breakup of viscoelastic liquid sheet.