A linear analysis method has been used to investigate the two-dimensional temporal instability behavior of viscoelastic liquid sheets of the parabolic velocity profile moving through the viscous ambient gas. The velocity profile of the liquid sheet and the gas boundary layer thickness were taken into account. It is seen that the velocity gradient of the viscoelastic liquid sheets is greater than that of the corresponding Newtonian ones. Moreover, the effects of the time constant, the elasticity number, and the liquid and gas Reynolds number on the velocity profile of the viscoelastic liquid sheets are researched. The relationship between growth rate and wave number of the disturbance wave was obtained with linear stability analysis and solved with a spectral method. The Theological parameters and flow parameters have been tested for their influences on the instability of the viscoelastic liquid sheets. The result reveals that the disturbances grow faster on the viscoelastic liquid sheets than on the Newtonian ones with the identical zero shear viscosity. Furthermore, the time constant, the liquid and gas Reynolds number, the Weber number, and the elasticity number have a great influence on the temporal stability of the viscoelastic liquid sheet.