In this paper, we analyze the performance of vehicle-to-vehicle (V2V) communication system, which employs full-duplex (FD) and energy harvesting (EH) techniques at source and relay nodes from power beacon (PB) through radio frequency. Unlike previous systemswhere all nodes located at fixed locations, we investigate the case that three nodes (source, relay,and destination) are moving vehicles. Therefore, the channels between them follow double (cascade) Rayleigh fading distributions. Furthermore, the source and relay nodes can harvest the energy from PB for data transmission when they move on the road. We derive the exact expressions of the outage probability (OP) and symbol error probability (SEP) of the proposed system and then intensively study the impacts of various parameters such as the number transmission antennas of PB, the time duration for EH, the distances between nodes, and the residual self-interference (RSI) at the FD relay node on the system performance. Monte-Carlo simulations validate all theory analysis. Numerical results show that system performance is strongly impacted by the number of transmission antennas of the power beacon, the EH duration, the RSI, and the distances between nodes. Moreover, for a given transmission of power beacon and the SIC capability of the FD relay node, there exist optimal EH duration and optimal distance from the source to relay, which provide the best system performance.