Neural-network-based (NN-based) planners have been increasingly used to enhance the performance of planning for autonomous vehicles. However, it is often difficult for NN-based planners to balance efficiency and safety in complicated scenarios, especially under real-world communication disturbance. To tackle this challenge, we present a safety-guaranteed framework for NN-based planners in connected vehicle environments with communication disturbance. Given any NN-based planner with no safety-guarantee, the framework generates a robust compound planner embedding the NN-based planner to ensure overall system safety. Moreover, with the aid of an information filter for imperfect communication and an aggressive approach for the estimation of the unsafe set, the compound planner could achieve similar or better efficiency than the given NN-based planner. A comprehensive case study of unprotected left turn and extensive simulations demonstrate the effectiveness of our framework.