In this letter, we present a single mixed-integer linear programming (MILP) model for high-stealth false data attacks (FDAs) on overloading a set of lines by injecting stealthy false data. The proposed model reveals that an intelligent attacker is able to deliberately construct a valid attack vector to overload multiple transmission lines while hiding it among normal data to evade advanced anomaly detection methods. In addition, the proposed cyber-attack mode can help the attacker optimally select the targeted lines. Simulation results on multiple large-scale test systems validate the effectiveness of the proposed approach.