We have theoretically analyzed the quasibound states in a graphene quantum dot (GQD) with a magneticflux Φ in the centre.It is shown that the two-fold time reversal degeneracy is broken and the quasibound states of GQDwith positive/negative angular momentum shifted upwards /downwards with increasing the magnetic flux.The variationof the quasibound energy depends linearly on the magnetic flux, which is quite different from the parabolic relationshipfor Schrdinger electrons.The GQD's quasibound states spectrum shows an obvious Aharonov-Bohm (AB) oscillationswith the magnetic flux.It is also shown that the quasibound state with energy equal to the barrier height becomes abound state completely confined in GQD.