Kernel-based learning presents a unified approach to machine learning problems such as classification and regression. The selection of a kernel and associated parameters is a critical step in the application of any kernel-based method to a problem. This paper presents a data-driven evolutionary approach for constructing kernels, named KTree. An application of KTree to the Support Vector Machine (SVM) classifier is described. Experiments on a synthetic dataset are used to determine the best evolutionary strategy, e.g. what fitness function to use for kernel evaluation. The performance of an SVM based on KTree is compared with that of standard kernel SVMs on a synthetic dataset and on a number of real-world datasets. KTree is shown to outperform or match the best performance of all the standard kernels tested.