A delayed choice experiment was done using the cold neutron spin interferometer of Jamin-type arrangement which is installed at the JRR-3M of JAERI. A pair of identical composite neutron mirrors composes the pair of the wave splitters of the interferometer. The composite neutron mirror consists of a Ni/Ti multilayer ((Ni: 85 Angstrom/Ti: 85 Angstrom) x 5 (layers)), a Ge gap layer (4000 Angstrom), and a Permalloy (Fe55Ni45)/Ge multilayer ((Permalloy: 85 Angstrom/Ge: 85 Angstrom) x 5 (layers)) (PGM), evaporated in series on the single Si wafer in a magnetic field of 130 G. The second composite mirror was placed in the pulsed magnetic field for producing the conditions of whether the second wave splitter is introduced or not when a polarized neutron reaches the second wave splitter. It was shown that whether the interference fringe is obtained or not depends only on whether the second wave splitter is introduced or not, after the neutron passed through the first wave splitter. Delaying choice has no effect on the interference. We could deduce that the neutron propagates both ways with equal probability after being split by the wave splitter and does not choose one of two ways, as explained by quantum mechanics. (C) 1998 Elsevier Science B.V. All rights reserved.