Magnetization of the frustrated S = 1/2 chain compound LiCuVO4, focusing on high magnetic field phases, is reported. Besides a spin-flop transition and the transition from a planar spiral to a spin modulated structure observed recently, an additional transition was observed just below the saturation field. This newly observed magnetic phase is considered as a spin nematic phase, which was predicted theoretically but was not observed experimentally. The critical fields of this phase and its dM/dH curve are in good agreement with calculations performed in a microscopic model (M. E. Zhitomirsky and H. Tsunetsugu, Europhys. Lett. 92, 37001 (2010)).