Abstract: The multi-group constants generated via continuous energy Monte Carlo method do not satisfy the equivalence between reference calculation and diffusion calculation applied in reactor core analysis. To the satisfaction of the equivalence theory, general equivalence theory (GET) and superhomogenization method (SPH) were applied to the Monte Carlo method based group constants, and a simplified reactor core and C5G7 benchmark were examined with the Monte Carlo constants. The results show that the calculating precision of group constants is improved, and GET and SPH are good candidates for the equivalence treatment of Monte Carlo homogenization.