1ES2344+514 (z = 0.04) is one of the rst BL Lac objects to be reported as an extreme synchrotron blazar withsynchotron peak energy reaching up to 100keV and was discovered as a source of Very High Energy (VHE)gamma- rays by the Whipple group in 1995. Subsequently, it was observed by the HEGRA group in 1997/98and 2002. We have recently (Oct.- Dec. 2004) observed the 1ES2344+514 using the imaging element of theTACTIC array and have collected data for 53 hours in on/off mode. The source was also observed in nearinfrared bands J, H and K, for some nights using NICMOS-3 array mounted on 1.2m MIRO infrared telescope.Such a study is expected to provide clues to the dominance or otherwise of the Compton component. Afterdetailed analysis of the TACTIC data we have placed an upper limit of    photons cmsata 3condence level on the gamma-ray ux from the source. In the near infrared band the source shows lowlevel variations without any aring activity.