Relative proper motions (PMs) and cluster membership probabilities (P_mu_) were derived for ~2500 stars in the field of the open star cluster NGC 3766. The cluster was observed in the B and V broad-band filters at two epochs separated by ~6yr using a wide-field imager mounted on the WFI@ESO 2.2-m telescope. All CCD frames were reduced using the astrometric techniques described by Anderson et al. (2006A&A...454.1029A, Paper I). The PM rms error for stars brighter than V~15mag is 2.0mas/yr, but it gradually increases up to ~4mas/yr at V~20mag. Using PM data, membership probabilities were derived for the stars in the region of the cluster. They indicate that one Ap and three Be stars are members of the cluster. A reddening of E(B-V)=0.22+/-0.05mag, a distance of 2.5+/-0.5kpc and an age of ~20Myr were derived using stars with P_mu_>70 per cent. A mass function slope of x=1.60+/-0.10 was derived for the cluster, and the cluster was found to be dynamically relaxed. Finally, we provide positions, calibrated B and V magnitudes, relative PMs and membership probabilities for the stars in the field of NGC 3766. We have produced a catalogue that is electronically available to the astronomical community.