The properties of the drift compressional instability in the magnetosphere with a two-component plasma are examined by using gyrokinetic theory. A dipole field is used to approximate the equilibrium geomagnetic field. In contrast to the slab model it is found that electrons of the hot component have a stabilizing effect on the mode excited by the protons. With appropriate vaues of various parameters, the wave periods in the range of 30--200 s are obtained from numerical calculations of the model. The drift compressional instability may provide possible explanation of the compressional waves observed in the magnetosphere.