A new method namely, dripping method is proposed for finding a set of efficient solutions to a bi-objective transportation problem which differs from all existing methods. The percentage level of satisfaction of a solution for a transportation problem is introduced. An illustrative example is presented to clarify the idea of the proposed approach. The dripping method can be served as an important tool for the decision makers to obtain efficient solutions, according to their level of satisfaction on the objective functions when they are handling various types of logistic problems involving two objectives.