We show a method to protect quantum states from the disturbance due to the random potential by successive rapid manipulations 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. The effective potential, which the quantum states feel, becomes uniform when the velocity of the transport is sufficiently large. It is also shown that the alternating transport of a Bose-Einstein condensate with the driving potential derived by fast-forward scaling theory [Masuda and Nakamura, Proc. R. Soc. A 466, 1135 (2010)] can protect it from the disturbance.