1. A road friction coefficient estimating apparatus for a vehicle comprising: an actual value estimating means for estimating an actual value of a vehicle motion parameter; a high friction coefficient road reference value estimating means for estimating a high friction coefficient road reference value of said vehicle motion parameter based on a vehicle motion model when said vehicle travels on a road surface with high friction coefficient; and a road friction coefficient estimating means for forming a Lissajou's figure based on said actual value and said high friction coefficient road reference value and for estimating a road friction coefficient according to a gradient and an area of said Lissajou's figure.