Epilepsy is a common neurological disorder of the brain and can be assessed by electroencephalogram (EEG). By combining discrete wavelet transformation (DWT) and weighted visibility graph (WVG), we employed a new approach for detecting epileptic seizure from EEG. First, DWT is applied to decompose EEG into different frequency bands, then WVG is constructed from the sub-band signals. Average weighted degree and clustering coefficient are extracted to characterize the topological structure of the networks and distinguish different brain states (healthy, inter-ictal and ictal). Four different test cases are designed to evaluate the performance of our DWT-WVG method. The obtained results demonstrate that both features are effective to discriminate the ictal EEG from interictal EEG or EEG recorded from healthy subjects.