Abstract: Neutron flux density in Accelerator Driven Subcritical reactor（ADS） is formed by superposition of fundamental and higher-order modes neutron flux density. Based on the bi-orthogonal properties of forward and ad-joint modes, modes expansion theory for steady state neutron flux density in ADS is established in this paper, and numerical studies on three dimensional four groups ADS diffusion problem are performed. Results indicate that both λ and prompt α modes can effectively re-construct the steady state neutron flux density of ADS, and neutron flux re-construction accuracy is improved by increasing expansion modes. Comparing to prompt α modes, λ modes are more appropriate for the steady state neutron flux density re-construction. Because of the symmetries of external neutron source and core pattern in this paper, only modes that have symmetrical properties have contributions to the steady state neutron flux density.