In order to accommodate additional plug-in electric vehicle (PEV) charging loads for existing distribution power grids, the vehicle-to-grid (V2G) technology has been regarded as a cost-effective solution. Nevertheless, it can hardly scale up to large PEVs fleet coordination due to the computational complexity issue. In this paper, a centralized V2G scheme with distributed computing capability engaging internet of smart charging points (ISCP) is proposed. Within ISCP, each smart charging point equips a computing unit and does not upload PEV sensitive information to the energy coordinator, to protect PEV users' privacy. Particularly, the computational complexity can be decreased dramatically by employing distributed computing, viz., by decomposing the overall scheduling problem into many manageable sub-problems. Moreover, six typical V2G scenarios are analyzed deliberately, and based on that, a load peak-shaving and valley-filling scheduling algorithm is built up. The proposed algorithm can be conducted in real-time to mitigate the uncertainties in arrival time, departure time, and energy demand. Finally, the proposed scheme and its algorithm are verified under the distribution grid of the SUSTech campus (China). Compared with uncoordinated charging, the proposed scheme realizes load peak-shaving and valley-filling by 11.98% and 12.68%, respectively. The voltage values are ensured within the limitation range by engaging power flow calculation, in which the minimum voltage values are increasing and the maximum voltage values are decreasing with the expansion of PEV penetration. What is more, the computational complexity of peak-shaving and valley-filling strategy is near-linear, which verifies the proposed scheme can be carried out very efficiently. K E Y W O R D S distributed computing, internet of smart charging points (ISCP), load peak-shaving and valleyfilling, plug-in electric vehicle, vehicle-to-grid