We report the results of our observations of HI absorption towards the central region of the rejuvenated radio galaxy 4C29.30 (J0840+2949) with the Giant Metrewave Radio Telescope (GMRT). The radio source has diffuse, extended emission with an angular size of $\sim$520 arcsec (639 kpc) within which a compact edge-brightened double-lobed source with a size of 29 arcsec (36 kpc) is embedded. The absorption profile which is seen towards the central component of the inner double is well resolved and consists of six components; all but one of which appears to be red-shifted relative to the optical systemic velocity. The neutral hydrogen column density is estimated to be $N$(HI)=4.7$\times10^{21}$($T_s$/100)($f_c$/1.0) cm$^{-2}$, where $T_s$ and $f_c$ are the spin temperature and covering factor of the background source respectively. This detection reinforces a strong correlation between the occurrence of HI absorption and rejuvenation of radio activity suggested earlier, with the possibility that the red-shifted gas is fuelling the recent activity.