Neutrinoless double beta decay has not been observed so far, and its existence cannot be disproved. Therefore the question whether neutrinos are Majorana particles is still inconclusive. In this paper, we hope to investigate the possibility of distinguishing neutrino fermion types by gravitational fields from the perspective of gravitational scattering of fermions. The Levi-Civita connection is decomposed according to the parity transformation. Under the perturbation therory of gravitational field to fermion quantum scattering and weak gravitational approximation, it is found that the difference between Dirac and Majorana fermion quantum scattering matrix elements of general metric gravitational field comes from similar vector parts under parity transformation; the scattering of the gravitational field on the Kerr metric confirms that the difference in scattering among different types of fermions is related to the angular momentum of the Kerr gravitational source, whose scattering matrix elements are proportional to the square of the product of the mass of the gravitational source and the angular momentum. The above results provide another possible way to distinguish fermion types by gravitational fields.