In this study, inviscid linear stability theory is used to investigate the compressibility effects of Batchelor vortices. The growth rates are obtained from asymptotic analysis with large wavenumbers, and it is shown that the growth of disturbances is affected largely by both the Mach number and the axial velocity deficit. From the maximum growth rates for various base flow conditions, the growth properties of Batchelor vortices are summarized reasonably by using a convective Mach number based on two relative Mach numbers for three-dimensional disturbances. In addition, the ratio of the circulation and velocity deficit at the maximum growth rate is closely related to the growth rate as a function of the convective Mach number because the correlation between the ratio and the growth rate is high when the Mach number is less than unity. Therefore, the compressibility effects, which are expressed as the relation between the growth property and the convective Mach number, are estimated simply from only the base flows (circulation and velocity deficit) in Batchelor vortices.