Unmanned aerial vehicles (UAVs) communications have been widely exploited in our daily life, which leads to rising concerns about the security issue. This work investigates the secrecy performance of a UAV-to-vehicle (UAV-2-V) communication system, where the information delivered over both downlink and uplink between a UAV (S) acting as a temporary aerial base-station and a legitimate vehicle (D) moving along a road is overheard by an eavesdropping vehicle (E) on the same road. The location of S is assumed to be uniformly distributed in the sky, while the locations of D and E are uniformly distributed on the highway. The statistical characteristics, including the cumulative distribution function and probability density function of the received signal-to-noise ratio over both downlink and uplink, are characterized respectively. Closed-form expressions for the approximate and asymptotic secrecy outage probability (SOP) of the downlink experiencing Rician fading channels have been derived accordingly. Moreover, the secrecy outage performance of the uplink is investigated by deriving the closed-form expression of the exact and asymptotic SOP in two cases: the eavesdropping channel suffers Rician and Weibull fading, respectively. Finally, Monte-Carlo simulations are shown to verify our proposed analytical models.