On a two-lane highway, vehicle-to-vehicle communication can provide drivers with the information that reflects the overall traffic situation within a local area. Such information may have significant influences on the driver’s perception of traffic condition as well as driving tasks. To explore the specific effects of such information on traffic stability, this paper proposes a Two-lane Local Optimality (TLO) driving strategy and develops a two-lane car-following model (TLO model) correspondingly. Analytical results indicate that TLO driving strategy can improve traffic stability. Simulation results agree well with the analytical ones. It is shown that the amplitudes of headway and velocity fluctuations are reduced in TLO model. The fluctuations become much smaller when the range of the local area is enlarged. All the results suggest that the TLO driving strategy has great potential for enhancing traffic stability. Moreover, the effectiveness of the strategy can be further strengthened as the local area increases within a certain range.