Buffer insertion is a popular technique to reduce the interconnect delay. The classic buffer insertion algorithm of van Ginneken has time complexity O(n^2), where n is the number of buffer positions. Lillis, Cheng and Lin extended van Ginneken's algorithm to allow b buffer types in time O (b^2 n^2). For modern design libraries that contain hundreds of buffers, it is a serious challenge to balance the speed and performance of the buffer insertion algorithm. In this paper, we present a new algorithm that computes the optimal buffer insertion in O (bn^2) time. The reduction is achieved by the observation that the (Q, C) pairs of the candidates that generate the new candidates must form a convex hull. On industrial test cases, the new algorithm is faster than the previous best buffer insertion algorithms by orders of magnitude.