This paper deals with a container terminal where containers are discharged by quay cranes from a ship and transported by a fleet of vehicles to the terminal yard. Since container terminals are fully utilized in general, It is important to increase terminal throughput by discharging the containers out of the ship without any delay, At the operational level, it should be decided which vehicle transports which container. The vehicle dispatching decision should be carefully made since the container discharging time increases when the quay cranes wait idle for the vehicles. This paper presents vehicle dispatching heuristics with the objective of minimizing the total container discharging time. The heuristics are based on a network flow model and a look-ahead concept. Through some experiments, the performance of the dispatching methods is evaluated.