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 neutro...