A split flow traffic flow lattice model on the road crossing was proposed, and the sufficient and necessary conditions for keeping the model's linear stability were derived. The MKdV equation was derived from the models near the critical point. By using the kink and anti kink solutions of the MKdV equation, the traffic jam was described. It is found that the coexisting curves decrease with the increasing of the rate of lane changing. Therefore, it plays stability role in heightening the traffic flows in main lane.