CANDECOMP/PARAFAC (CP) tensor factorization of incomplete data is a powerful and useful data analysis technique. This method can achieve the purpose of tensor completion through explicitly capturing the multilinear latent factors. Recently, a CP factorization based on a hierarchical probabilistic model has been proposed which is used fully Bayesian theory by incorporating a sparsity-inducing prior over multiple latent factors and the appropriate hyper-priors over all hyper-parameters. In this way, the rank of tensor can be determined automatically instead of traditional manual assignment. This method has been applied into image inpainting and facial image synthesis effectively. However, there is no research on the application in EEG signal processing of this method. Moreover, the EEG data loss often occurs during experiment recording period. In this paper, we used this newer data analysis method for processing EEG data set from P300 experiment including data completion under different levels of data missing and classification analysis on the recovered data. The experiment result shows that this method has a good processing performance on incomplete EEG signal.