The ability to detect motion and track a moving object hidden around a corner or behind a wall provides a crucial advantage when physically going around the obstacle is impossible or dangerous. Previous methods have demonstrated that it is possible to reconstruct the shape of an object hidden from view. However, these methods do not enable the tracking of movement in real time. We demonstrate a compact non-line-of-sight laser ranging technology that relies on the ability to send light around an obstacle using a scattering floor and then detect the return signal from a hidden object within only a few seconds of acquisition time. By detecting this signal with a single-photon avalanche diode (SPAD) camera, we follow the movement of an object located a metre away from the camera with centimetre precision. We discuss the possibility of applying this technology to a variety of real-life situations in the near future.