Abstract: Using two nuclear models, i) the relativistic continuum Hartree-Bogoliubov (RCHB) theory and ii) the Weizsäcker-Skyrme (WS) model WS^*, the performances of nine kinds of kernel functions in the kernel ridge regression (KRR) method are investigated by comparing the accuracies of describing the experimental nuclear charge radii and the extrapolation abilities. It is found that, except the inverse power kernel, all other kernels can reach the same level around 0.015~0.016 fm for these two models with KRR method. The extrapolation ability for the neutron rich region of each kernel depends on the trainning data. Our investigation shows that the performances of the power kernel and Multiquadric kernel are better in the RCHB+KRR calculation, and the Gaussian kernel is better in the WS^*+KRR calculation. In addition, the performance of different basis functions in the radial basis function method is also investigated for comparison. The results are similar to the KRR method. The influence of different kernels on the KRR reconstruct function is discussed by investigating the whole nuclear chart. At last, the charge radii of some specific isotopic chains have been investigated by the RCHB+KRR with power kernel and the WS^*+KRR with Gaussian kernel. The charge radii and most of the specific features in these isotopic chains can be reproduced after considering the KRR method.