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Abstract. We consider the problem of computing the time-convex hull of a point set under the general Lp metric in the presence of a straight-line highway in the plane. The traveling speed along the highway is assumed to be faster than that off the highway, and the shortest time-path between a distant pair may involve traveling along the highway. The time-convex hull TCH(P ) of a point set P is the smallest set containing both P and all shortest time-paths between any two points in TCH(P ). In this paper we give an algorithm that computes the time-convex hull under the Lp metric in optimal O(n log n) time for a given set of n points and a real number p with 1 ≤ p ≤ ∞.