Abstract: A new continuum traffic flow dynamics model for freeways with two lanes where the faster vehicles are allowed to travel on both lanes while the slower vehicles are allowed to travel on the slower lane only, is developed through applying the speed gradient-based momentum equation for each lane. Some non-equilibrium phenomena of traffic flow such as small disturbance instability and stop-and-go waves can be reproduced by the new continuum model. The wave properties of the new model, which include shock waves, rarefaction waves and first order wave of the two lanes, are respectively studied. The numerical results show that the model respectively reflects the shock waves and rarefaction waves of the two lanes, and the figures about first order wave speeds of the two lanes respectively describe the stop-and-go traffic on both lanes. This study can further help understand the complicated driving behavior and the nonlinear properties of traffic flow dynamics on multilane freeways, and then improve the traffic control and management.