We report radial velocities for 99 galaxies with projected positions within 30 arcmin of the center of the cluster A3733 obtained with the MEFOS multifiber spectrograph at the 3.6-m ESO telescope. These measurements are combined with 39 redshifts previously published by Stein (1996) to built a collection of 112 galaxy redshifts in the field of A3733, which is used to examine the kinematics and structure of this cluster. We assign cluster membership to 74 galaxies with heliocentric velocities in the interval 10500-13000 km/s. From this sample of cluster members, we infer a heliocentric systemic velocity for A3733 of 11653{+74}{-76} km/s, which implies a mean cosmological redshift of 0.0380, and a velocity dispersion of 614{+42}{-30} km/s. The application of statistical substructure tests to a magnitude-limited subset of the latter sample reveals evidence of non-Gaussianity in the distribution of ordered velocities in the form of lighter tails and possible multimodality. Spatial substructure tests do not find, however, any significant clumpiness in the plane of the sky, although the existence of subclustering along the line-of-sight cannot be excluded.