The one-to-all broadcast is the most primary operation in a multicomputer network. In this paper, we consider this problem in a wormhole-routed 2D torus network which provides the dimension-ordered routing and all-port communication capability. With the distance-insensitive characteristic of wormhole routing, we model the broadcast as a sequence of communication phases. We propose a novel scheme to solve this problem. The scheme requires at most two communication phases more than the optimal number of phases when the torus is square, or at most four or five communication phases more than optimum when the torus is nonsquare. The best known results, as compared to ours, can only be applied to square tori of very restricted network sizes and either rely on an undesirable non-dimension-ordered routing or require more numbers of phases.