We numerically analyze the dynamic behavior of Bose-Einstein condensate (BEC) in a one-dimensional disordered potential before it completely loses spatial quantum coherence.We find that both the disorder statistics and the atom interactions produce remarkable effects on localization.We also find that the single phase of the initial condensate is broken into many small pieces while the system approaches localization,showing a counter-intuitive step-wise phase but not a thoroughly randomized phase.Although the condensates as a whole show less flow and expansion,the currents between adjacent phase steps retain strong time dependence.Thus we show explicitly that the localization of a finite size Bose-Einstein condensate is a dynamic equilibrium state.In nature,disordered systems exist more generally than periodic ones,because impurities and defects are always present,and disorder is indeed an intrinsic property of all real systems.Although sometimes the strength of disorder is much smaller than the chemical potential of a system,it still produces remarkable effects in the system.