The preferential orientation of martensitic variants in the single crystal Ni-52 Mn-24 Ga-24 has been characterized by various methods, such as optical microscopy observation, strain measurement, and magnetic field - induced strain (MFIS). The origin of the spontaneous preferential orientation of variants was attributed to the internal stress with a magnitude of about 2.45 MPa, as calculated based on the experimental data. We found that the preferential orientation of variants produced the anisotropy, different effective elastic constants and distribution of magnetic domain, between two equivalent crystallographic directions of [001] and [010]. The resulting MFIS properties, such as saturated MFIS, saturated field, hysteresis effect and initial magnetic field have been discussed in detail.