The effects of compressibility on the Rayleigh-Taylor instability in Z-pinch implosion plasmas are investigated by means of simple slab geometry. The linear mode equation, which includes main steady-state quantities and their gradients, is derived. Numerical solutions are presented. The incompressible fluid result is also obtained. These results indicate that the linear growth rate of the Rayleigh-Taylor instability for the compressible magnetohydrodynamic fluid is far larger than one in the incompressible situation. Therefore, the compressible systems are all more unstable than the incompressible ones.