The electroencephalogram (EEG) has been extensively used to record brain signals for the analysis of neurological diseases over several decades. Epilepsy is the one of the most common neurological disorder in the world. It is associated with seizures, which are a clinical manifestation of abnormal, excessive excitation and synchronisation of a population of cortical neurons, resulting in abrupt changes in consciousness, movement, behaviour, and feelings. Our goal in this letter is to propose a computationally efficient EEG based system that can detect seizures with improved detection performance. To deeply optimize the electrodes and frequency bands, we proposed a fast computational algorithm by finding the critical electrodes and optimal sub-bands of EEG signals. We used wavelet packet decomposition (WPD) to find optimal sub-bands and maximum relevance minimum redundancy (mRMR) method for electrodes selection. It is found that the portrait of the features in the phase space depicted promising discriminating ability to detect seizure efficiently. Experimental results show that the proposed method outperformed the state-of-art methods and provided 100% and 94.79% of detection accuracy on UBonn and CHB-MIT datasets, respectively, at a significantly reduced computational cost.