We investigated the time lags and the evolution of the cross spectrua of Z source GX 5-1, observed by Rossi X-ray Timing Explorer (RXTE), when it is in the horizontal branch oscillations. We showed that the time lags of 3 horizontal branch oscillations are related to the position on the hardness intensity diagram. 3 QPOs were shown to be of the hard time lags. But on the cross spectra, one is in a “dip”, one in a “bump”, another has not that chracteristic. The time lags of two of the QPOs decrease with QPO's frequency, and one has a trend increasing with its freuqency. In the normal branch, we found that there is no significant time lags in the present observational data.