Abstract: Compared with critical reactor, more asymmetric distribution of neutron flux, higher average energy of neutron, more complex neutron spectrum and larger variation of neutron importance inside an ADS sub-critical reactor make the traditional point kinetic equation difficult to simulate the neutron dynamics of such a sub-critical reactor realistically. Firstly, the kinetic equations governing the neutron flux and precursor in a multigroup neutron energy model and their adjoint equations were introduced. Then, the kinetic equations with normalized reactor power were derived based on the steady state diffusion equation and its adjoint equation. Additionally, the point kinetic equations with source neutron importance were derived with the definition of some operators. Finally, the equations were verified by several simple cases. The research establishes the foundation of the further analysis for ADS sub-critical reactor dynamics.