Abstract: Compared with the critical reactor, the distributions of source neutron and fission neutron are asymmetric inside ADS (accelerator driven sub-critical system) sub-critical reactor, as well as the importance function is different. The multigroup-diffusion approximation was used to simplify the steady-state transport equation into multigroup equation. Then an adjoint equation normalized by the power of reactor core and an importance function associated with the relative power were derived. The physical significance of neutron importance in the sub-critical reactor was also derived. Finally, two different expressions of multiplication factor for sub-critical reactor with external neutron source were derived based on steady-state adjoint equations.