In this paper, the authors present an analytical model to determine the network connectivity probability of a linear vehicular Ad-hoc NETwork (VANET) formed by communication equipped vehicles on a two-way street scenario. They consider the highway to be consisting of two lanes with vehicles moving in both directions on these lanes and focus on the probability of being able to convey messages from a source vehicle to a destination vehicle, which may be multiple hops away. Closed form analytical expression is obtained for the network connectivity probability in the presence of Nakagami fading channel. In their model, the transmission range of each vehicle is modeled as a random variable due to channel fading. The analytical results are validated by extensive simulations.