Accurate channel prediction is essential for addressing channel aging caused by user mobility. However, the actual channel variations over time are highly complex in high-mobility scenarios, which makes it difficult for existing predictors to obtain future channels accurately. The low accuracy of channel predictors leads to difficulties in supporting reliable communication. To overcome this challenge, we propose a channel predictor based on spatio-temporal electromagnetic (EM) kernel learning (STEM-KL). Specifically, inspired by recent advancements in EM information theory (EIT), the STEM kernel function is derived. The velocity and the concentration kernel parameters are designed to reflect the time-varying propagation of the wireless signal. We obtain the parameters through kernel learning. Then, the future channels are predicted by computing their Bayesian posterior, with the STEM kernel acting as the prior. To further improve the stability and model expressibility, we propose a grid-based EM mixed kernel learning (GEM-KL) scheme. We design the mixed kernel to be a convex combination of multiple sub-kernels, where each of the sub-kernel corresponds to a grid point in the set of pre-selected parameters. This approach transforms non-convex STEM kernel learning problem into a convex grid-based problem that can be easily solved by weight optimization. Finally, simulation results verify that the proposed STEM-KL and GEM-KL schemes can achieve more accurate channel prediction. This indicates that EIT can improve the performance of wireless system efficiently.