Over 50 million people all over the world are suffering from epilepsy It is of great significance to achieve automatic seizure detection in electroencephalogram (EEG) signal for clinical diagnosis and treatment. In order to achieve automatic diagnosis of epilepsy, a multitude of automated computer aided diagnostic techniques have been proposed. However, only a few of studies lay emphasis on the effects of different rhythm signals. To explore the influence of rhythm signals on classification accuracy, a newly-developed time-frequency analysis method called frequency slice wavelet transform (FSWT), which is able to locate arbitrary time-frequency range with the use of frequency slice function and whose inverse transformation only relies on fast Fourier transform, is employed to extract five different rhythm signals, namely (0.5-4 Hz), (4-8 Hz), (8-13 Hz), (13-30 Hz) and (30-50 Hz) from original EEG signal. Subsequently, for extracting the nonlinear and linear features, the approximate entropy of each rhythm signal and fluctuation index of adjacent rhythm signals are calculated to reflect the variation characteristics of rhythm signals and they are flocked together to form the nine-dimensional feature vectors. Finally, the extracted vectors are fed into a support vector machine (SVM) which is optimized by genetic algorithms (GA) for classification. Specifically, since the parameters of SVM are associated with the final classification accuracy and appropriate parameters could lead to a remarkable result, GA is applied to parameter optimization, half of the obtained vectors are randomly selected as a training set for training, and the remaining vectors constitute a testing set to test the established model. Experimental results of the proposed approach, which is employed in a public epileptic EEG dataset obtained from department of epitology at Bonn University for validation indicate that the proposed method in this study can carry out the task of classifying normal, inter-ictal and epileptic seizure EEG signals with a high classification accuracy (98.33%), a sensitivity of 99%, a specificity of 99%, and a positive predictive value of 99.5%. The presented approach provides an outstanding scheme for the automatic diagnosis of epilepsy, and the directions of our further research may include the application of the proposed method to the diagnosis of other disorders.