We show a method to protect quantum states from the disturbance due to the random potential using successive transport of the quantum states. The quantum states are kept undisturbed for a longer time than the case of the simple trapping with a stationary potential because the effective potential, which the quantum states feel, becomes uniform when the velocity of the transport is sufficiently large. It is shown that a Bose-Einstein condensate is protected from the disturbance by the alternating transport using the fast forward scaling theory [Masuda and Nakamura, Proc. R. Soc. A 466, 1135 (2010)].