In this paper, we construct a Bessel-class kernels for Support Vector Machine. This new class of kernels are proved that they are continuous and satisfy Mercer’s condition. The presented Bessel-class kernels can degenerate to Gaussian kernel in an infinite smooth case. Compared to the other kernels, these present Bessel kernels can be flexibly applied to classification and regression with fewer constants to be adjusted. Additionally, four simulation experiments including classifications and regressions, have been carried out to show the good performance of these Bessel-class kernels.