Kernel grower is a novel kernel clustering method proposed recently by Camastra and Verri. It shows good performance for various data sets and compares favorably with respect to popular clustering algorithms. However, the main drawback of the method is the weak scaling ability in dealing with large data sets, which restricts its application greatly. In this paper, we propose a scaled-up kernel grower method using core-sets, which is significantly faster than the original method for large data clustering.Meanwhile, it can deal with very large data sets. Numerical experiments on benchmark data sets as well as synthetic data sets show the efficiency of the proposed method. The method is also applied to real image segmentation to illustrate its performance.