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We consider intermittently connected vehicular networks (ICVNs) in which base stations (BSs) are installed along the highway to connect moving vehicles with internet. Due to the deployment cost, it is hard to cover the entire highway with BSs. To minimize the outage time in the uncovered area (UA), several cooperative store-carry-forward (CSCF) schemes have been proposed in which a vehicle is selected to act as a relay by buffering data to be relayed to a target vehicle in the UA. In this paper, we propose an energy-efficient full-duplex (FD) CSCF scheme that exploits the relay ability to receive and transmit simultaneously to improve the effective communication time, Te, between the relay and the target vehicle. Accordingly, it can minimize the outage time and deliver more data to the the target vehicle. In addition, the power allocation that minimizes the transmission cost (TC) under the required rates constraints is found. The problem is formulated as a geometric program (GP) and globally solved using the interior-point method. As compared to the half-duplex CSCF scheme, simulation results show that the proposed FD scheme offers more effective time, more successfully delivered data in the UA and lower TC.