Functional Data Analysis (FDA) is devoted to the study of data which are functions. Support Vector Ma- chine (SVM) is a benchmark tool for classification, in particular, of functional data. SVM is frequently used with a kernel (e.g.: Gaussian) which involves a scalar bandwidth parameter. In this paper, we pro- pose to use kernels with functional bandwidths. In this way, accuracy may be improved, and the time intervals critical for classification are identified. Tuning the functional parameters of the new kernel is a challenging task expressed as a continuous optimization problem, solved by means of a heuristic. Our experiments with benchmark data sets show the advantages of using functional parameters and the ef- fectiveness of our approach.