Context: The connection of cluster mergers with the presence of extended, diffuse radio sources in galaxy clusters is still being debated. Aims: We aim to obtain new insights into the internal dynamics of Abell 959, showing evidence of a diffuse radio source, analyzing velocities and positions of member galaxies. Methods: Our analysis is based on redshift data for 107 galaxies in the cluster field acquired at the Telescopio Nazionale Galileo. We also use photometric data from the Sloan Digital Sky Survey (Data Release 6). We combine galaxy velocities and positions to select 81 galaxies recognized as cluster members and determine global dynamical properties. We analyze the cluster searching for substructures by using the weighted gap analysis, the KMM method and the Dressler-Shectman statistics. We also study the 2D galaxy distribution in the field of the cluster. We compare our results with those from X-ray and gravitational lensing analyses. Results: We estimate a cluster redshift of = 0.2883±0.0004. We detect an NE high velocity group at 5' from the cluster center with a relative line-of-sight (LOS) velocity of ~ +1900 km s-1 with respect to the main system. We also detect a central, dense structure elongated along the SE-NW direction likely connected with the two dominant galaxies and their surrounding cores. This elongated central structure is probably the trace of an old cluster merger. The LOS velocity dispersion of galaxies is very high. By excluding the NE clump we obtain σV = 1025-75+104 km s-1 and a virial mass M(