Seeking effective measures to characterize the chaotic patterns of EEG signals for seizure diagnosis is a long-term endeavor in the literature. We propose to count the number of zero-crossing (ZC) points on Poincaré surface as a feature when the time series of interest is embedded into the reconstructed state space. The experiments show that Poincaré surface can act as a platform to observe the chaotic patterns of EEG signals and the ZC feature on Poincaré surface is a promising pattern descriptor to discriminate different categories of EEG signals. When used alone for EEG classification, the ZC feature achieves 100%, 99.27%, and 94.68% accuracy in 2-class, 3-class, and 5-class classification on a widely used benchmark.