Betatron radiation in strongly magnetized plasma is investigated by two dimensional (2D) particle-in-cell (PIC) simulations. The results show that the betatron radiation in magnetized plasmas is strongly enhanced and is more collimated compared to that in unmagnetized plasma. Single particle model analysis shows that the frequency and the amplitude of the electrons's betatron oscillation are strongly influenced by the axial external magnetic field and the axial self-generated magnetic field. And the 2D PIC simulation shows that the axial magnetic field is actually induced by the external magnetic field and tends to increase the betatron frequency. By disturbing the perturbation of the plasma density in the laser-produced channel, the hosing instability is also suppressed, which results in a better angular distribution and a better symmetry of the betatron radiation.