This paper considers a dual-hop vehicle-to-vehicle (V2V) communication system equipped with full-duplex relays (FDRs) in the millimeter-wave networks. The performance of this network is studied in a dense multi-lane highway considering cooperative best vehicular relay selection strategy. In fact, two different FDR schemes are analyzed for the given network. In the first scheme that is called self-interference (SI) vehicle relaying selection, the FDR models the source-relay and the relay-relay links by one channel state information (CSI) coefficient (i.e., a single channel estimation of the two links), while in the second scheme that is called individual SI vehicle relaying selection, the CSI of the source-relay and the relay-relay links are estimated separately. Moreover, relay-destination link is modeled by one CSI coefficient in both aforementioned schemes. Dissimilar to traditional V2V schemes where either line-of-sight (LOS) or non-line-of-sight (NLOS) propagation is considered, and the effect of the blockage on V2V communications is not taken into account when analyzing the performance, in this paper, we propose a probabilistic model capturing the occurrences of LOS and NLOS propagations, which depend on the movement of the vehicles between the central and adjacent lanes. Thus, the movement of the vehicles between any two adjacent lanes is assumed to take place independently and is deemed to be according to the Poisson distribution. This vehicle movement model considers the blockage between the source and destination links. In this vein, a LOS link is considered available when the center lane is clear of vehicles between the source and destination nodes, and an NLOS link is assumed otherwise. Furthermore, a Nakagami-m fading channel model is considered due to its excellent representation of the V2V communication environment. The LOS/NLOS probabilities combined together with the probability of blockage are used to analyze the system performance. The cumulative density function expression of the signal-to-interference-plus-noise ratio at the relay is derived for both relaying schemes. Moreover, the lower bound expressions of the end-to-end outage probabilities are developed and used to express throughput. Finally, the theoretical results postulated and presented here are verified by the numerical simulation for a variety of parameters.