A new higher-order continuum model is proposed by considering the coupling and lane changing effects of the vehicles on two adjacent lanes. A stability analysis of the proposed model provides the conditions that ensure its linear stability. Issues related to lane changing, shock waves and rarefaction waves, local clustering and phase transition are also investigated with numerical experiments. The simulation results show that the proposed model is capable of providing explanations to some particular traffic phenomena commonly observable in real traffic flows. A new higher-order continuum model is proposed by considering the coupling and lane changing effects of the vehicles on two adjacent lanes. Issues related to lane changing, shock waves and rarefaction waves, local clustering and phase transition are also investigated with the established experiments is also investigating in the simulations of real traffic flows.