  We investigate the influence of a strong magnetic field on various properties
of neutron stars with quark-hadron phase transition. The one-gluon exchange
contribution in a magnetic field is calculated in a relativistic
Dirac-Hartree-Fock approach. In a magnetic field of $5\times 10^{18}$G in the
center of the star, the overall equation of state is softer in comparison to
the field-free case resulting in the reduction of maximum mass of the neutron
star.
