There are generally two kinds of traffic control strategies to relieve traffic congestion in lanedrop bottlenecks: variable speed limits (VSL) control and lane-changing (LC) control. However, VSL has limited or even no effect due to many mandatory LC maneuvers near bottlenecks, while LC fails to reduce traffic congestion when traffic demand is high. Although a few control methods combine VSL and LC, they do not consider the interaction between VSL and LC, which rules out many potentially good alternatives. We instead propose an integrated VSL and LC control method under a connected and automated vehicle (CAV) environment, which can consider the interaction and simultaneously find the values of LC numbers and speed limits to maximize traffic efficiency. Our control is in the framework of the model predictive control (MPC), which consists of prediction, optimization, and implementation. We adopt an improved multiclass cell transmission model (CTM) for traffic state prediction, then use the genetic algorithm (GA) for optimization which optimizes traffic network performance, and implement our control method in the SUMO platform. Simulation results demonstrate that our control method greatly improves the capacity of the road and is robust to different traffic demands and scenarios. Our control outperforms no control and VSL-only control in travel time and exhaust emissions, which reduces total travel time by 23.86% to 44.62% and exhaust emissions by 10.29% to 48.19%. INDEX TERMS Connected and automated vehicles (CAVs), lane-changing (LC) control, lane-drop bottlenecks, variable speed limits (VSL).