Since Einstein, Podolsky and Rosen suggested in the thirties and nowadays known as an EPR-paradox, non-local correlations between sufficiently separated subsystems have been extensively discussed. From a theoretical point of view, such a non-locality can be interpreted as a consequence of the correlation between commuting observables. A more general concept, i.e. contextuality, compared to non-locality can be introduced to describe striking phenomena predicted by quantum theory. As the first example, a neutron interferometer experiment is presented, where the spin and the path degrees of freedom are used to exhibit the clear violation of a Bell-like inequality. Other aspects of the quantum contextuality is reported, e.g. a flavor of Kochen-Specker-like contradiction in neutron optical experiments. In addition, the quantum state tomography of the Bell states, which are used in the experiments, is shown.