Personal identification is particularly important in information security. There are numerous advantages of using electroencephalogram (EEG) signals for personal identification, such as uniqueness and anti-deceptiveness. Currently, many researchers focus on single-dataset personal identification, instead of the cross-dataset. In this paper, we propose a method for cross-dataset personal identification based on a brain network of EEG signals. First, brain functional networks are constructed from the phase synchronization values between EEG channels. Then, some attributes of the brain networks including the degree of a node, the clustering coefficient and global efficiency are computed to form a new feature vector. Lastly, we utilize linear discriminant analysis (LDA) to classify the extracted features for personal identification. The performance of the method is quantitatively evaluated on four datasets involving different cognitive tasks: (i) a four-class motor imagery task dataset in BCI Competition IV (2008), (ii) a two-class motor imagery dataset in the BNCI Horizon 2020 project, (iii) a neuromarketing dataset recorded by our laboratory, (iv) a fatigue driving dataset recorded by our laboratory. Empirical results of this paper show that the average identification accuracy of each data set was higher than 0.95 and the best one achieved was 0.99, indicating a promising application in personal identification.