In a travelling road estimating apparatus, an estimator estimates, based on the coordinates of at least one of edge points included in a selected candidate, a road parameter using a previously prepared filter having an adjustable response level. The road parameter is associated with a condition of the travelling road relative to the vehicle and a shape of the travelling road. A determiner determines whether there is an unstable situation that causes an accuracy of estimating the edge points by an edge extractor to be reduced. A response level adjuster adjusts the response level of the filter in accordance with determination of whether there is an unstable situation that causes an accuracy of estimating the edge points by the edge extractor to be reduced.