CCD BV photometry to V=20.5 of stars in the old open cluster NGC 6791 is presented. Comparison with the theoretical isochrones of VandenBerg gives a cluster age in the range of 10 to 12.5Gyr, and an apparent distance modulus of 13.45mag, adopting a solar metallicity. This cluster is only marginally younger than Palomar 12, which is the youngest globular cluster known. A search for short-period variables in the cluster field led to the discovery of only one low-amplitude variable, probably belonging to the FK Com-type stars. A very blue star was detected which may be an extremely young white dwarf formed in the cluster.