We have made the Heusler-type Ni
_2
MnGa-based alloys, Ni
_{2.18}
Mn
_{0.82}
Ga, Ni
_{2.19}
Mn
_{0.81}
Ga and Ni
_2
Mn
_{0.92}
Ga
_{1.08}
, which have the martensitic transformation temperature coincident with the Curie temperature. The powder neutron diffraction measurements of these alloys were performed. The Rietveld analysis of the diffraction patterns showed that at least two crystal structures coexist in each martensitic phase. For Ni
_{2.18}
Mn
_{0.82}
Ga and Ni
_{2.19}
Mn
_{0.81}
Ga, the main structure is a monoclinic one with a six-layers shuffling and a small amount of orthorhombic structure distorted from the cubic Heusler one is included. For Ni
_2
Mn
_{0.92}
Ga
_{1.08}
, the main structure is tetragonal whereas a small amount of other structures seem to be included. The neutron diffraction of Ni
_{2.19}
Mn
_{0.81}
Ga under magnetic field up to 5 T at the coincident transformation temperature of 350 K shows that the magnetic field causes the phase transformation from cubic phase to martensitic one. The result suggests the possibility of controlling the shape memory effect originating from the thermoelastic martensitic transformation, by applying the external magnetic field instead of changing the temperature.