We propose to perform a neutron diffraction experiment under magnetic fields using a single crystal sample of multiferroic alpha-NaFeO2 on WISH beamline. Recently, we have suggested a novel mechanism for the higher-order bilinear magnetoelectric effect in this compound from our powder neutron diffraction measurements [N. Terada et al, PRB 89 184421 (2014)]. The mechanism implies a field-induced symmetry-lowering of the incommensurate propagation vector, which is from a line of symmetry to a general point. The mechanism is very general and is relevant to all classes of multiferroics. To unambiguously confirm the mechanism, a single crystal experiment is necessary. Recently, Prof. Sato?s group has succeeded in growing high-quality alpha-NaFeO2 single crystals. In this study, we propose to directly explore the effect of the magnetic field on the incommensurate propagation vectctor.