We succeeded in detecting neutrons using superconducting tunnel junctions (STJs) fabricated on a single crystal of Li2B4O7. Neutrons are captured in the crystal by the nuclear reactions 6Li+n→T+alpha+4.78MeV and 10B+n→7Li+alpha+2.3MeV, which excite a large number of phonons in the substrate. The phonons propagate in the absorber and are measured by the STJs. We selected a single crystal of Li2B4O7 as the absorber material because of properties such as the large neutron cross-section of 6Li and 10B, low γ-ray sensitivity, short particle range in the substrate, and fast phonon velocity. Series-connected or multiple STJs on the crystal would enable two-dimensional neutron imaging with high detection efficiency, low γ-ray background, and a high spatial resolution of a few microns. In this paper, we demonstrate neutron detection by STJs and report the basic characteristics of the fabricated STJs, including their X-ray response and neutron detection. The correlation in pulse heights between two junctions located ∼1.3mm apart clearly indicates the possibility of neutron imaging.