Considering all the ground-state atom interactions, we investigate the population transfer of two Bose-Einstein condensate (BEC) states, which are trapped in different potential wells, or two ground states of the BEC in the same trap using the stimulated Raman adiabatic process. With a proper choice of pulsed geometric parameters,the dark state exists. By simply choosing ground-state detunings, the effects of the interatomic interaction can be suppressed and a high population transfer rate can be obtained.