We study the cross-correlation between X-rays of different energies for the atoll-type source 4U 1608–52 with RXTE, and find the cross-correlation evolutes along the different branches. The anti-correlation is reported from the Galactic black hole candidates and Z-type luminous sources in their hard states. Our results are a little different from the Z-type sources. Here we provide the first evidence that a similar anti-correlated feature can also be found in atoll-type source, and it is not corresponding to the lowest accretion rate.