This paper considers a supervised image segmentation algorithm based on joint-kernelized structured prediction. In the proposed algorithm, correlation clustering over a superpixel graph is conducted using a non-linear discriminant function, where the parameters are learned by a kernelized-structured support vector machine (SSVM). For an input superpixel image, correlation clustering is used to predict the superpixelgraph edge labels that determine whether adjacent superpixel pairs should be merged or not. In previous works, the discriminant functions for structured prediction were generally chosen to be linear with the model parameter and joint feature map. However, the linear model has two limitations: complex correlations between two input-output pairs are ignored, and the joint feature map should be explicitly designed. To cope with these limitations, a nonlinear discriminant function based on a joint kernel, which eliminates the need for explicit design of the joint feature map, is considered. The proposed joint kernel is defined as a combination of an image similarity kernel and an edge-label similarity kernel, which measure the resemblance of two input images and the similarity between two edge-label pairs, respectively. Each kernel function is designed for fast computation and efficient inference. The proposed algorithm is evaluated using two segmentation benchmark datasets: the Berkeley segmentation dataset (BSDS) and Microsoft Research Cambridge dataset (MSRC). It is observed that the joint feature map implicitly embedded in the proposed joint kernel performs comparably or even better than the explicitly designed joint feature map for a linear model.