Knowledge of the stellar content near the Sun is important for a broad range of topics ranging from the search for planets to the study of Milky Way (MW) structure. The most powerful method for identifying potentially nearby stars is proper motion (PM) surveys. All old optical surveys avoid, or are at least substantially incomplete, near the Galactic plane. The depth and breadth of the 'VISTA Variables in Via Lactea' (VVV) near-IR survey significantly improves this situation. Taking advantage of the VVV survey data base, we have measured PMs in the densest regions of the MW bulge and southern plane in order to complete the census of nearby objects. We have developed a custom PM pipeline based on VVV catalogues from the Cambridge Astronomy Survey Unit, by comparing the first epoch of JHKs with the multi-epoch Ks bands acquired later. Taking advantage of the large time baseline between the Two Micron All Sky Survey (2MASS) and the VVV observations, we also obtained 2MASS-VVV PMs. We present a near-IR PM catalogue for the whole area of the VVV survey, which includes 3003 moving stellar sources. All of these have been visually inspected and are real PM objects. Our catalogue is in very good agreement with the PM data supplied in IR catalogues outside the densest zone of the MW. The majority of the PM objects in our catalogue are nearby M-dwarfs, as expected. This new data base allows us to identify 57 common PM binary candidates, among which are two new systems within 30 pcof the Sun.