Ni-Ti alloys are typical shape-memory materials. It is suggested that the atomic-scale phase transformation between martensite and austenite crystalline phases is responsible for such function. However, it is reported that these alloys sometimes show also amorphization together with nanocrystal under severe deformation. The mechanism of amorphization should compete against martensitic (crystalline) transformation (MT). This study focuses on the atomistic relation between amorphization and MT in Ni-Ti alloys. Molecular dynamics simulation is performed by using our simplified potential built on the MEAM framework. The change in crystalline state is identified and traced mainly by developing common neighbor analysis (CNA) method. Under amorphization from B2 cubic structure, the characteristic topological change in CNA cluster around a transforming atom is detected. By applying simple shear in periodic specimen, it is found that the martensite phases appear first then amorphous phases are formed. The nucleation of amorphous phases is strongly dependent on choice of shear plane, e.g. {100}, {110} or {111} plane. When the shear direction does not match to the orientation of inherent slip system, amorphous phase is nucleated with relative ease and remains for a long time. It is recognized that dislocation slip (plastic deformation), MT and amorphization are closely related in atomic scale. The direction of phase transition is mostly "B2(austenite)"→"B19'(martensite)"→"amorphous", except for the case of {111} shear plane which possesses "pre-amorphous" structures. It is found that the "pre-amorphous" is once formed and then disappears, preceding martensite phase or principal and later formation of amorphous phase.