The magnetocrystalline anisotropy in a single-crystal Co 37Ni34Al29 ferromagnetic shape-memory alloy has been investigated. The prestrain was applied to the parent phase in order to nucleate the specific variant in the sample cooled down through the martensitic transformation temperature. The applied magnetic field facilitates the growth of variants parallel to the applied magnetic field in analogy with the prestrain. From these results of selective nucleation of variants, the magnetocrystalline anisotropy energy in the single crystal Co37Ni34Al 29 β′ martensite phase is estimated to be 3.9×106erg/cm3. In the single crystal, the observed magnitude of the reversible magnetic-field-induced strains is 0.06%.