We propose a novel carbon fiber-based conductive silicone sponge for low electrode-skin impedance EEG recordings. When this sponge is used with water or saline solution, no gel is required, lowering the setup time drastically compared to classical wet electrodes. Moreover, the wet conductive carbon fiber silicone sponges achieve an electrode-skin impedance as low as $2.5\mathrm {k} \Omega $ at 1kHz when wet, making them better than state of the art gel electrodes. Additionally, even as the sponge dries out, it continues to remain conductive and performs as a reliable dry electrode. We demonstrate through experiments that these conductive carbon fiber silicone sponge electrodes, wet or dry, are able to measure alpha wave activity. Our carbon fiber conductive sponge electrodes are low-cost and are highly suitable for designs of portable high density EEG measurement systems.