We propose a novel patient-specific method for predicting epileptic seizures by analysis of positive zero-crossing intervals in scalp electroencephalogram (EEG). In real-time analysis, the histogram of these intervals for the current EEG epoch is computed, and the values which correspond to the bins discriminating between interictal and preictal references are selected as an observation. Then, the set of observations from the last 5 min is compared with two reference sets of data points (interictal and preictal) using a variational Gaussian mixture model (GMM) of the data, and a combined index is computed. Comparing this index with a patient-specific threshold, an alarm sequence is produced for each channel. Finally, a seizure prediction alarm is generated according to channel-based information. The proposed method was evaluated using ~40.3 h of scalp EEG recordings from 6 patients with total of 28 partial seizures. A high sensitivity of 95% was achieved with a false prediction rate of 0.134/h and an average prediction time of 22.8 min for the test dataset.