A low-powered implantable device that could detect a pre-seizure state using intracranial EEG (iEEG) could provide significant improvement in quality of life for people with epilepsy. In our previous work, we proposed a prediction algorithm using 27-54 linear features of spectral power and nonlinear support vector machine (SVM) classification. Though the algorithm can produce high prediction rate, it may suffer from its high complexity and may not be feasible for an implantable device. In this study, we have lowered the complexity of the algorithm by examining small numbers of key features and replacing the nonlinear SVM with linear one. The key features for seizure prediction have been determined using a method of two-step recursive feature elimination using SVMs (RFE SVM). The proposed reduced-complexity algorithm uses 6 or 9 key features of spectral power, the linear SVM, and a 20-point moving-average postprocessing filter. It has been out-of-sample tested on 9 subjects on the Freiburg database that we demonstrated high prediction rate with the full 27-54 features in our previous work. The reduced-complexity algorithm with 6 time-differential features has demonstrated high sensitivity of 100.0% (38 of total 38 preictal events), low false positive (FP) rate of 0.15 per hour (total 32 FPs), and FP time of 9.65% (21.0-hour) in the 217.5-hour interictal recordings. With 9 time-differential key features, it has achieved sensitivity of 97.4% (37/38), FP rate of 0.11/hour (25 FPs), and FP portion of 6.95% (15.1-hour). The proposed algorithm demonstrates that high prediction rate can be maintained while significantly lowering complexity. Our proposed methods for reducing complexity can be expanded to other biomedical engineering applications, especially where key feature determination with respect to accuracy and complexity is necessary.