We have developed new types of neutron spin echo interferometer based on a coherent superposition of the two eigen states of ↑ and ↓ neutron spins in a magnetic field, similar to a neutron spin echo spectrometer. By means of the neutron interferometer, we have observed spin precession of neutron through a magnetic layer in tunneling region, a magnetic Fabry-Perot film in a bound state of ↑ spin neutron, a magnetic multilayer at Bragg condition and a helical single crystal of holmium at magnetic Bragg condition. The observed spin precessions are well reproduced by the phase differences of ↑ and ↓ spin wave-functions of neutron solved by Schrödinger equation based on the one dimensional rectangular magnetic potentials.