Kelvin-Helmholtz instability in two-dimensional compressible fluid is analyzed by the high precision numerical scheme. The linear growth rate of the Kelvin-Helmholtz instability is especially explored. The relations among the initial static pressure, conductive Mach number and linear growth rate of the Kelvin-Helmholtz instability are quantitatively achieved at the case of the low and high Mach numbers. The simulation results agree with the experiment results in free shear layers and mixing layers. Simulation results show that the conductive Mach number is the proper parameter in definition the compression effect. The smaller the conductive Mach number is, the less compressible the fluid is. The linear growth rate of the Kelvin-Helmholtz instability decreases with the increasing conductive Mach number.