Electroencephalogram (EEG) signal based early diagnosis of Alzheimer's Disease (AD), especially a discrimination between healthy control (HC) and mild cognitive impairment (MCI) has received remarkable attentions to complement conventional diagnosing methods in clinical fields. A relative power (RP) metric which quantifies the abnormal EEG pattern 'slowing' has widely been used as a major feature to distinguish HC and MCI, however, the optimal spectral ranges of the RP are influenced by the given dataset. In this study, we proposed the deep neural network based classifier using the RP to fully exploit and recombine the features through its own learning structure. The DNN enhanced the diagnosis results compared to shallow neural network, and enabled to interpret the results as we used the wellknown RP features as the domain knowledge. We investigated and explored the potentials of DNN based detection of the earlystage AD.