Investigations on entanglement between degrees of freedom (DOF) of neutrons successfully confirmed quantum contextuality: the violation of a Bell-like inequality, Kochen-Specker-like phenomena, and characteristics of tripartite Greenberge-Horne-Zeilinger (GHZ) state have been observed. In addition, recent experiments concerning the tripartite entanglement successfully approve a linear form of the entanglement witness: so-called Greenberger-Horne-Zeilinger (GHZ) as well as W states are generated and used for the experiments. In parallel, we achieved a new spin-manipulation method using a Mu-metal pipe and a radio-frequency (RF) spin-flipper to entangle efficiently the spin DOF, which exhibit quite high efficiency of the manipulation. By using these new progresses, we are going to perform an experiment, which is expected to provide clearer and higher violation of Bells inequality with spin-path bipartite entanglement in neutrons.