We present multiple GPU computing with the common unified device architecture (CUDA) for the Swendsen-Wang multi-cluster algorithm of two-dimensional (2D) q-state Potts model. Extending our algorithm for single GPU computing [Y. Komura, Y. Okabe, CPU-based Swendsen-Wang multi-cluster algorithm for the simulation of two-dimensional classical spin systems, Comput. Phys. Comm. 183 (2012) 1155-1161], we realize the CPU computation of the Swendsen-Wang multi-cluster algorithm for multiple GPUs. We implement our code on the large-scale open science supercomputer TSUBAME 2.0, and test the performance and the scalability of the simulation of the 2D Potts model. The performance on Tesla M2050 using 256 GPUs is obtained as 37.3 spin flips per a nano second for the q = 2 Potts model (Ising model) at the critical temperature with the linear system size L = 65536. (C) 2012 Elsevier B.V. All rights reserved.