Short bunch beams of high intensity are required by many applications, and they are usually obtained by using bunch compression before the extraction in relatively slow cycling synchrotrons or accumulator rings. In this article, short bunch extraction by the bunch compression method is proposed to apply to a rapid cycling synchrotron (RCS) where the time duration is very limited to exploit the bunch compression process. The method is practically applied in the RCS of the China Spallation Neutron Source (CSNS) to obtain short-bunch beams for white neutron applications. Different short-bunch extraction scenarios have been studied, from keeping full beam power to reduced beam powers. A special desynchronization method is designed to solve the problem of slow acceleration during the bunch rotation process when the magnetic field is still ramping up. The space charge effect and beam loading effect during the bunch compression have also been taken into account in this high-intensity RCS. Multiparticle simulations have been carried out to show the effectiveness of the method with the input of the CSNS RCS. With a sacrifice of about twothirds of the beam power, the rms bunch length of the extracted beam can be reduced to about one-ninth of the one in the nominal operation mode.