Purpose: We propose a patient-specific algorithm for seizure prediction using multiple features of spectral power from electroencephalogram (EEG) and support vector machine (SVM) classification. Methods: The proposed patient-specific algorithm consists of preprocessing, feature extraction, SVM classification, and postprocessing. Preprocessing removes artifacts of intracranial EEG recordings and they are further preprocessed in bipolar and/or time-differential methods. Features of spectral power of raw, or bipolar and/or time-differential intracranial EEG (iEEG) recordings in nine bands are extracted from a sliding 20-s-long and half-overlapped window. Nine bands are selected based on standard EEG frequency bands, but the wide gamma bands are split into four. Cost-sensitive SVMs are used for classification of preictal and interictal samples, and double cross-validation is used to achieve in-sample optimization and out-of-sample testing. We postprocess SVM classification outputs using the Kalman Filter and it removes sporadic and isolated false alarms. The algorithm has been tested on iEEG of 18 patients of 20 available in the Freiburg EEG database who had three or more seizure events. To investigate the discriminability of the features between preictal and interictal, we use the Kernel Fisher Discriminant analysis. Key findings: The proposed patient-specific algorithm for seizure prediction has achieved high sensitivity of 97.5% with total 80 seizure events and a low false alarm rate of 0.27 per hour and total false prediction times of 13.0% over a total of 433.2 interictal hours by bipolar preprocessing (92.5% sensitivity, a false positive rate of 0.20 per hour, and false prediction times of 9.5% by time-differential preprocessing). This high prediction rate demonstrates that seizures can be predicted by the patient-specific approach using linear features of spectral power and nonlinear classifiers. Bipolar and/or time-differential preprocessing significantly improves sensitivity and specificity. Spectral powers in high gamma bands are the most discriminating features between preictal and interictal. Significance: High sensitivity and specificity are achieved by nonlinear classification of linear features of spectral power. Power changes in certain frequency bands already demonstrated their possibilities for seizure prediction indicators, but we have demonstrated that combining those spectral power features and classifying them in a multivariate approach led to much higher prediction rates. Employing only linear features is advantageous, especially when it comes to an implantable device, because they can be computed rapidly with low power consumption.