Mesh-based interconnection networks are the most popular inter-processor communication infrastructures used in current parallel supercomputers. Although many analytical models of n-D torus interconnection networks have been reported in the literature over the last decade, few analytical models have been proposed for the 2-D mesh case (and not for the general n-D mesh network) using inaccurate approximations as they have not fully incorporated the asymmetry effects of the mesh topology, in order to reduce the model complexity. There has not been reported, to the best of our knowledge, a performance model that can deal with the n-D mesh network. To fill this gap, in this paper, we propose the first analytical performance model of the n-D mesh using adaptive wormhole routing. To this end, we calculate the exact traffic rates over different network channels and determine the average message latency by averaging over the message latency values corresponding to all possible source-destination pairs of nodes in the network. Simulation results show that the proposed model can predict the message latency fairly accurately under various working conditions.