Recognizing characters extracted from natural scene images is quite challenging due to the high degree of intraclass variation. In this paper, we propose a multi-scale graph-matching based kernel for scene character recognition. In order to capture the inherently distinctive structures of characters, each image is represented by several graphs associated with multi-scale image grids. The similarity between two images is thus defined as the optimum energy by matching two graphs (images), which finds the best match for each node in the graph while also preserving the spatial consistency across adjacent nodes. The computed similarity is suitable to construct a kernel for support vector machine (SVM). Multiple kernels acquired by matching graphs with multi-scale grids are combined so that the final kernel is more robust. Experimental results on challenging Chars74k and ICDAR03-CH datasets show that the proposed method performs better than the state of the art methods.