Aiming at the problems of low accuracy, poor universality and functional singleness for seizure detection, an effective approach using wavelet-based non-linear analysis and genetic algorithm optimized support vector machine (GA-SVM) is proposed to deal with five challenging classification problems in this study. Instead of the traditional discrete wavelet transform (DWT), we attempt to explore the ability of double-density discrete wavelet transform (DD-DWT) to decompose the original EEG into specific sub-bands. The Hurst exponent (HE) and fuzzy entropy (FuzzyEn) are extracted as input features and then fed into two classifiers. On using these ranking non-linear features, the GA-SVM configured with fewer features is found to achieve the prominent classification performance for various combinations such as AB-CD-E, A-D-E, ABCD-E, C-E and D-E, achieving accuracies of 99.36%, 99.60%, 99.40%, 100% and 100%, respectively. The results have indicated that our scheme is not only appropriate in solving problems with multiple classes but also of lower complexity and better expansibility. These characteristics would make this method become an attractive alternative for actual clinical diagnosis.