A unique transient bursting radio source, GCRT J1745−3009, has been discovered near the direction of the Galactic Centre. The explanation of this phenomenon is still an open question, although some efforts to understand its nature have been made. This Letter shows that most of the observed features can be reproduced by our proposed precessing pulsar model. It is found that the precession angle of the pulsar should be larger (≳15°) than that of previously known precessing pulsars, which have a precession angle ≲10°, if the beam width of the pulsar is larger than 10°. The pulsar could be a nulling (or even extremely nulling) radio pulsars to account for the transient nature of the source. This model can be confirmed if a pulsar is detected at the position of the source. The pulsar could hardly be a normal neutron star (but could probably be a solid quark star) if the spin period of the pulsar is detected to be ≳10 ms in the future.