The Hg2CuTi-type structure is found to be preferable energy wise than the Cu2MnAl-type structure for full-Heusler Cr2MnAl and exhibits half-metallic ferromagnetism based on first principles. The calculations for the mixed compounds with disorder between B and D sublattices reveal that the case of exchanging one atom maintains the half-metallicity while the case of exchanging two atoms loses it. The electronic structures of the atoms at sites A or C are affected mainly by the nearest-neighboring coordination while that of the atoms at site B are determined by the next-nearest-neighboring coordination.