We simulate the distribution of neutral hydrogen (HI) at the redshifts z D 1:3 and 3:4 using a cosmological N-body simulation along with a prescription for assigning HI masses to the particles. The HI is distributed in clouds whose properties are consistent with those of the damped Lyman- absorption systems (DLAs) seen in quasar spectra. The clustering properties of these clouds are identical to those of the dark matter. We use this to simulate the redshifted HI emission expected at 610 MHzand 325 MHz, two of the observing bands at theGMRT. These are used to predict the correlations expected between the complex visibilities measured at different baselines and frequencies in radio-interferometric observations with the GMRT. The visibility correlations directly probe the power spectrum of HI fluctuations at the epoch when the HI emission originated, and this holds the possibility of using HI observations to study large-scale structures at high z.