  We investigate the properties of strange quark matter in a strong magnetic
field with quark confinement by the density dependence of quark mass
considering the total baryon number conservation, charge neutrality and
chemical equilibrium. The strength of the magnetic field considered in this
article is $10^{16} \sim 10^{20}$ G. It is found that an additional term should
appear in the pressure expression to maintain thermodynamic consistency. At
fixed density, the energy density of magnetized strange quark matter varies
with the magnetic field strength. The exists a minimum with increasing the
field strength, depending on the density. It is about $6\times10^{19}$ Gauss at
two times the normal nuclear saturation density.
