Various positioning techniques such as Wi-Fi positioning system have been proposed to use in situations where satellite navigation is unavailable. One such system, the muometric positioning system (muPS), was invented for navigation which operates in locations where even radio waves cannot reach such as underwater or underground. muPS takes advantage of a key feature of its probe, cosmic-ray muons, which travel straightforwardly at almost a speed of light in vacuum regardless of the matter they traverse. Similar to other positioning techniques, muPS is a technique to determine the position of a client's muPS receiver within the coordinate defined by reference detectors. This can be achieved either by using time-of-flight (ToF) or angle of arrival (AoA) measurements. The latter configuration (AoA), called the Vector-muPS has recently been invented and the present paper describes the developments of the first prototype of a vector muometric wireless navigation system (MuWNS-V) with this new vector-muPS concept and its demonstration. With MuWNS-V, the reference tracker and the receiver ran wirelessly with fully independent readout systems, and a positioning accuracy of 3.9 cm (RMS) has been achieved. We also evaluated the outcome of measuring continuous indoor localization of a moving receiver with this prototype. Our results indicated that further improvements in positioning accuracy will be attainable by acquiring higher angular resolution of the reference trackers. It is anticipated that "sub-cm level" navigation will be possible for muPS which could be applied to many situations such as future autonomous mobile robot operations.