We synthesized the off-stoichiometric Heusler-type alloys, Ni2.18Mn0.82Ga and Ni2.19Mn0.81Ga, which have a thermo-elastic martensitic transformation temperature coincident with a Curie temperature, 340K and 350K, respectively. The single crystal of this alloy shows a shape memory effect. From the Rietveld analysis of powder neutron diffraction experiments, we found that the martensitic phase of the alloys consists of two crystal structures. One is an orthorhombic structure and the other is a tetragonal structure, both of them are distorted from a cubic Heusler structure. Each structure is constructed from a shuffling of the each other structure. The shape memory effect of a single crystal occurred when the mass fractions of martensitic phase and the mother phase become fifty-fifty. By the neutron diffraction of a single crystal, we were able to determine the direction of the crystal growth and to observe the structure change accompanied to the martensitic transformation. From the powder neutron diffraction under the magnetic field, we confirmed that the external magnetic field causes the transformation from paramagnetic mother phase to ferromagnetic martensitic phase. To control the shape memory effect by external magnetic field becomes realistic.