  The quark quasiparticle model is extended to study the properties of
color-flavor locked strange quark matter at finite chemical potential and in a
strong magnetic field. We present a self-consistent thermodynamic treatment by
employing a chemical potential dependent bag function. It is found that the
magnetized color-flavor-locked (MCFL) matter is more stable than other phases
within a proper magnitude of magnetic field. The stability window is
graphically shown for the MCFL matter compared with ordinate magnetized matter.
The anisotropic structure of MCFL matter is dominated by the magnetic field and
almost independent of the energy gaps. A critical maximum magnetic field of
about $1.56\times 10^{18}$ G is found, under which MCFL matter is absolutely
stable with respect to nuclear matter.
