Shape memory effect in MnFeCu antiferromagnetic alloy comes from the FCC-FCT martensitic transformation (MT). Compared with many other alloys, MnFeCu alloys have small lattice distortion. The infinitesimal deformation (ID) approach theory was applied to study the crystallography of FCC-FCT MT with the twinning shear as the lattice invariant shear in the MnFeCu alloy. Simple analytical solutions were derived, which were in good agreement with the experiment results. Compared the calculated results with those obtained from the classical WLR theory, it was found that the former are the approximation by neglecting the higher-order terms of the latter. In the condition of small lattice distortion, they almost have the same accuracy. Therefore, for the alloys with small lattice distortion, ID approach theory can be applied to predicate the crystallography conveniently, which can derive simple analytical solutions with high accuracy. ©, 2015, Central South University of Technology. All right reserved.