With {it RXTE} data, we analyzed the cross-correlation function between the soft and hard X-rays of the transient atoll source 4U 1608-52. We found anti-correlations in three outbursts occurred in 1998, 2002 and 2010, and significant time lags of several hundreds of seconds in the latter two outbursts. Our results show no correlation between the soft and hard X-rays in the island state, and a dominated positive correlation in the lower banana state. Anti-correlations are presented at the upper banana state for the outburst of 2010 and at the lower left banana states for the other two outbursts. So far for atoll sources the cross-correlation has been studied statistically only for 4U 1735-44, where anti-correlations showed up in the upper banana state. Here our investigation upon 4U 1608-52 provides a similar result in its 2010 outburst. In addition, we notice that the luminosities in the upper banana of 1998 and 2002 outbursts are about 1.5 times that of 2010 outburst whose luminosity in the upper banana is close to that of 4U 1735-44. The results suggest that the states in color-color diagram of a source could be correlated with the luminosity of the source. A further spectral analysis shows that, during the 2010 outburst, although an anti-correlation presents at the highest fluxes, the contemporary spectrum is not the softest one along the outburst evolution. This suggests that the observed anti-correlation may be relevant to the transition between the hard and soft states, which is consistent with the previous results on 4U 1735-44 and several black hole X-ray binaries that anti-correlations are observed during the transition states.
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