We present a catalogue of velocities for 551 galaxies (and give the coordinates of 39 stars misclassified as galaxies in our photometric plate catalogue) in a region covering about 100'x100' (0.94x0.94Mpc for an average redshift of 0.0555, assuming H_0_=50km/s/Mpc) in the direction of the rich cluster ABCG85. This catalogue includes previously published redshifts by Beers et al. (1991AJ....102.1581B) and Malumuth et al. (1992AJ....104..495M), together with our 367 new measurements. A total of 305 galaxies have velocities in the interval 13350-20000km/s, and will be considered as members of the cluster. ABCG 85 therefore becomes one of the clusters with the highest number of measured redshifts; its optical properties are being investigated in a companion paper.