In conventional sliding electrical contacts (SECs), large critical current density (CCD) requires a high ratio between actual and apparent contact area, while low friction and wear require the opposites. Structural superlubricity (SSL) has the characteristics of zero wear, near zero friction, and all-atoms in real contact between the contacting surfaces. Here, we show a measured current density up to 17.5 GA/m^{2} between microscale graphite contact surfaces while sliding under ambient conditions. This value is nearly 146 times higher than the maximum CCD of other SECs reported in literatures (0.12 GA/m^{2}). Meanwhile, the coefficient of friction for the graphite contact is less than 0.01 and the sliding interface is wear-free according to the Raman characterization, indicating the presence of the SSL state. Furthermore, we estimate the intrinsic CCD of single crystalline graphite to be 6.69 GA/m^{2} by measuring the scaling relation of CCD. Theoretical analysis reveals that the CCD is limited by thermal effect due to the Joule heat. Our results show the great potential of the SSL contacts to be used as SECs, such as micro- or nanocontact switches, conductive slip rings, or pantographs.