We give a fast algorithm for computing Jones polynomials of 2-bridge links. Given the Tait graph with n edges of a 2-bridge diagram, this algorithm runs with O(n) additions and multiplications in polynomials of degree O(n), namely in O(n(2) log n) time. We also propose an algorithm that, given the Tait graph with n edges of a closed 3-braid diagram, computes the Jones polynomial of the closed 3-braid link in O(n(2) log n) time. (C) 2006 Elsevier B.V. All rights reserved.