Considering the primary vortex in front of the pier to be the prime agent causing scour at bridge piers, a scheme has been proposed for computation of the temporal variation of scour depth during live-bed condition. An equation has also been developed for the computation of maximum scour depth around circular bridge piers in uniform sediments during live-bed condition. The equation follows logically from the scheme proposed for the computation of the temporal variation of scour. The effect of unsteadiness of flow on scour depth has been also studied.