To solve the traffic safety problem caused by the emergency lane change of the front vehicle to the target lane during lane changing of a network-connected autonomous vehicle. By considering the lane line and road boundary constraints as well as the collision risk between the network-connected autonomous vehicle and the obstacle vehicle, a lane-changing critical collision model was established. The lane change trajectory with safety constraints was planned by integrating the lane change critical model and polynomial planning method. Further to reduce the reaction time of emergency obstacle avoidance for the connected vehicle and improve the dynamic response effect of the avoidance trajectory, the reachability analysis method was used to search out the safe region and the polynomial was used to plan the safe avoidance trajectory. Finally, for specific real traffic scenarios, numerical simulation analysis of the planned trajectory was carried out using MATLAB, and the simulation results show that the lane-changing trajectory satisfies the constraints of safety, comfort, and lane-changing efficiency, and the planned avoidance trajectory can satisfy the requirements of safety under the premise of sacrificing part of the comfort and reduce the safety risk of the vehicle facing the unexpected situation.