The temporal instability analysis on the shear layer formed by injecting nitrogen jet into the supercritical nitrogen environment was carried out. The instability solution of the supercritical shear layer was obtained by using a spectral high precision, numerical method. The real gas effect of the base flow was calculated by using the Soave-Redlich-Kwong equation of state. The dependence of the viscosity with the pressure and temperature was fitted from the NIST REFPROP physical properties. The influence of the different thermodynamic parameters on the temporal instability of the supercritical shear layer was investigated, and the magnitude and distribution of the eigenvalues were analyzed. The results showed that the instability was restrained with the increase in the pressure. With a constant velocity ratio, the temporal instability increased with the increased velocity. With a constant temperature ratio, the temporal instability also increased with the increased temperature. With the other parameters kept constant, the instability of the shear layer was dependent on the value of vertical bar T-infinity - T-infinity vertical bar . The growth rate increased with the increase in the velocity ratio. The distribution of eigenvalues and their relationships with the parameters of flow field were discussed.