Classification of electroencephalogram (EEG) is a crucial issue for EEG-based brain computer interface (BCI) system. In this paper, the performances of the Gaussian process classifier (GPC) for three different categories of EEG signals, i.e. steady state visually evoked potential (SSVEP), motor imagery and finger movement EEG data, are investigated. The main purpose of this paper is to explore the practicability of GPC for EEG signals classification of different tasks. Compared with some commonly employed algorithms, the GPC achieves similar or better performances. Furthermore, the probabilistic output provided by the GPC can also be of great benefit to the decision making for both online and offline EEG analysis.