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The properties of color-flavor locked strange quark matter in an exteal strong magnetic field are investigated in a quark model with density-dependent quark masses. Parameters are determined by stability arguments. It is found that the minimum energy per baryon of the color-flavor locked (MCFL) matter decreases with increasing magnetic-field strength in a certain range, which makes MCFL matter more stable than other phases within a proper magnitude of the exteal magnetic field. However, if the energy of the field itself is added, the total energy per baryon will increase.