We present the results of our comprehensive study of the Galactic open star cluster NGC 6866. The positions of stars in the investigated region have been obtained with the "Fantasy "automatic measuring machine from 10 plates of the normal astrograph at the Pulkovo Astronomical Observatory. The size of the investigated field is 40x40arcmin^2^, the limiting magnitude is B<=16.6mag, and the maximum epoch difference is 79yr. For 1202 field stars we have determined the relative proper motions with a rms error of 0.5mas/yr. Out of them 413 stars may be considered cluster members with a probability P>70% according to the astrometric criterion. Photometric diagrams have been used as an additional criterion. We have performed two-color BV CCD photometry of stars with the Pulkovo ZA-320M mirror astrograph. The U magnitudes from the literature have also been used to construct the two-color diagrams. A total of 267 stars have turned out to be members of NGC 6866 according to the two criteria. We present refined physical parameters of the cluster and its age estimate (5.6x10^8^yr). The cluster membership of red and blue giants, variable, double, and multiple stars is considered. We have found an almost complete coincidence of the positions of one of the stars in the region (a cluster nonmember) and a soft X-ray source in the ROSAT catalog. The "Fantasy " automatic measuring machine is described in the Appendix. DOI:10.1134/S106377371005004X