Phase transformation behavior and shape memory characteristics of a Ti-44.7Ni-5Cu-0.3Mo(at%) alloy were investigated. The two stages B2-B19-B19' transformation occurred in a Ti-44.7Ni-5Cu-0.3Mo alloy. The B19 martensite in a Ti-44.7Ni-5Cu-0.3Mo alloy did not involve the characteristic internal defects usually observed in martensites as a result of a lattice-invariant deformation, since the principal lattice distortions themselves satisfy the invariant plain strain condition. Substitution of Mo for Ni in a Ti-45Ni-5Cu alloy increased the critical stress for slip deformation and the pseudoelastic recovery. The maximum recoverable elongation of a Ti-44.7Ni-5Cu-0.3Mo alloy was 6.4%.