We present the results of a photometric survey for variable stars in the central region of the nearby globular cluster NGC 6397. Time-series photometry was obtained for 30 variable objects. The sample includes 12 new objects, of which six show periodic light curves and two are eclipsing binaries of unknown period. Six variables possess certain and three possess likely X-ray counterparts detected with the Chandra observatory. Among them, four are cataclysmic variables and one is a foreground eclipsing binary. The cataclysmic variable CV2 exhibited a likely dwarf nova type outburst in 2003 May. The cataclysmic variable CV3 was observed at 18.5 22. We have found that the light curve of the optical companion to the millisecond pulsar PSR J 1740-5340 exhibits noticeable changes of its amplitude on a time-scale of a few months. A shallow eclipse with AV = 0.03 mag was detected in one of the cluster turn-off stars suggesting the presence of a large planet or brown dwarf in orbit.