The Monte Carlo intra-nuclear cascade program CBIM has been developed for describing spallation reactions involving protons, neutrons and pions on complex nuclei. In order to describe cascade process, several simplifications and assumptions are made in the following:firstly, neither reaction, nor reflection, nor refraction, nor ionization will be taken into account before the incident particle enters into the target nucleus; secondly, target nucleus is regarded as being spherical and the atom number should be greater than 2; thirdly, the knocked nucleon is determined by cross section sampling; finally, in the center-of-mass frame, the scattering angle is sampled based on differential cross section distribution. The basis physics model is based on the above assumptions and Bertini intra-nuclear cascade model; meanwhile, nucleon-nucleon angle differential distributions of INCL in the center-of-mass frame are introduced to overcome the shortage of Bertini model. The interactions between nucleon and nucleon or between nucleon and pion, such as elastic scattering, pion production and charge exchange, are included in the code. In the particles collision, the nucleon density changes with the target nucleus radius; and the interaction cross sections refer to 22 kinds of experimental cross sections in Bertini model. The intra-nuclear cascades induced by 45-3500 MeV neutron, proton or pion below 2500 MeV can be simulated by this code. Finally, comparisons between experimental reaction cross section over the energy range 60-378 MeV, and some simulation results by MCNPX, GEANT4 and PHITS over the energy range 65-3000 MeV show that they are in reasonable agreement with the CBIM results over the broad energy range considered.