The results of a comprehensive study of the Galactic open cluster NGC 6800 are presented. The positions of stars to a limiting magnitude B<=16.5mag in an 80x80 arcmin field centered at the cluster were measured on eight plates from the Pulkovo normal astrograph with a maximum epoch difference of 57 years. The measurements were performed with the Pulkovo "Fantasy" automated measuring system. The corresponding field from the 2MASS catalogue was used as an additional plate. As a result, the relative proper motions of stars were obtained with a root-mean-square error of 3.0 mas/yr. A catalogue of BV and JHK magnitudes for objects in the investigated region was compiled from available published resources. The astrometric selection of cluster members was made by the maximum likelihood method. An individual cluster membership probability of a star P>=60% served as the first selection criterion. The position of a star on the photometric color-magnitude (V-(B-V)), J-(J-Ks)) diagrams was considered as the second selection criterion. On the basis of these criteria, it was established that 109 stars are members of NGC 6800. These data were used to refine the physical parameters of the cluster: the mean reddening E(B-V)=0.40mag, the true distance modulus (V-Mv)0=10.05mag, and the cluster age ~250Myr. The luminosity and mass functions were constructed. The position of the center of the cluster NGC 6800 was improved: RA=19:27:11.2 and DE=+25:07:24 (2000).