This article reports on the spatial-temporal instability behavior of a supercritical shear layer considering the real-gas effect. The dispersion relation governing the pressure perturbation was obtained and utilized to study the spatial-temporal instability of a shear layer. The dispersion relation was solved using a shooting method. The results are presented with a view to the effects of temperature ratio, velocity ratio, oblique angle, and Mach number. It is shown that in some cases, the variation of dimensionless numbers would lead to a transition between absolute and convective instability. A large value of temperature ratio or velocity ratio would enhance absolute instability; that is, increased temperature ratio or velocity ratio can make the supercritical shear layer transit to absolutely instability. Study of the effects of the oblique angle of disturbance waves shows that in spatial-temporal mode, three-dimensional disturbances dominate over two-dimensional disturbances. Increased compressibility would damp the absolute instability of a supercritical shear layer.