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We report the detections of the anti-correlated soft and hard X-rays, and the time lags of $\sim$ hecto-second from the neutron star low-mass X-ray binary Cyg X-2, a well-known Z-type luminous source. Both the anti-correlation and the positive correlation were detected during the low-intensity states, while only the latter showed up during high-intensity states. Comparing with the lower part of normal branch and flaring branch, more observations located on the horizontal and the upper normal branches are accompanied with the anti-correlation, implying the occurrence of the anti-correlation under circumstance of a low mass accretion rate. So far the anti-correlated hard lag of thousand-second timescale are only reported from the Galactic black hole candidates in their hard states. Here we provide the first evidence that a similar feature can also establish in a neutron-star system like Cyg X-2. Finally, the possible origins of the observed time lags are discussed under the current LMXB models.