A wireless electroencephalogram (EEG) sensor using a stretchable electrode sheet and electrode-tissue impedance measurement module is presented herein. The sensor can be attached to the forehead using biocompatible gel with the electrode sheet. The sensor is compactly designed for 3 cm × 9 cm × 6 mm with weight of 12 g. Impedance scanning circuit is also proposed to evaluate the skin surface condition before EEG measurements. We developed the impedance scanning board for 3 cm × 5 cm × 3 mm, with weight of 5.6 g. Results show that the proposed system demonstrates a promising performance in diagnosing the Alzheimer's disease using frequency domain analysis.