We have fabricated overdamped NbN Josephson junctions based on Nb/AlOx/Nb trilayer technology. The junctions have the structure of NbN/Nb/AlOx/Nb/NbN, where Nb/AlOx/Nb acts as a junction barrier. The overdamped junctions showed a critical current density Jc and characteristic voltage as high as 0.44 kA/cm2 and 160 µV at 10 K, respectively. The junction characteristics at 4.2 K were investigated from the viewpoint of their dependence on the film thickness of the Nb layers. The junction uniformity was also evaluated. The standard deviation, 1-σ, was 2.1% for a series of 64 5×5 µm2 junctions at 4.2 K.