  We present a catalogue of 261 new infrared selected members of the 3C129
galaxy cluster. The cluster, located at $z \approx$ 0.02, forms part of the
Perseus-Pisces filament and is obscured at optical wavelengths due to its
location in the zone of avoidance. We identified these galaxies using the $J-$
and $K-$band imaging data provided by the UKIDSS Galactic Plane Survey within
an area with a radius of $1.1^{\circ}$ centred on the X-ray emission of the
cluster at $\ell, b \approx 160.52^{\circ}, 0.27^{\circ}$. A total of 26 of the
identified galaxy members have known redshifts 24 of which are from our 2016
Westerbork HI survey and two are from optical spectroscopy. An analysis of the
galaxy density at the core of the 3C129 cluster shows it to be less dense than
the Coma and Norma clusters, but comparable to the galaxy density in the core
of the Perseus cluster. From an assessment of the spatial and velocity
distributions of the 3C129 cluster galaxies that have redshifts, we derived a
velocity of $cz = 5227 \pm 171$ km/s and $\sigma = 1097 \pm 252$ km/s for the
main cluster, with a substructure in the cluster outskirts at $cz = 6923 \pm
71$ km/s with $\sigma = 422 \pm 100$ km/s. The presence of this substructure is
consistent with previous claims based on the X-ray analysis that the cluster is
not yet virialised and may have undergone a recent merger.
