In ordinary transportation problems, it is always supposed that the mileage from every source to every destination is a definite number. But in special conditions, such as transporting emergency materials when natural calamity occurs or transporting military supplies during wartime, the carrying network may be destroyed, mileage from some sources to some destinations are no longer definite. It is uncertain, a grey number. In these conditions, transportation capacity is often poor; the problems of optimization become even more important. In this paper, we proposed a new method to find an optimal solution for grey transportation problems where transportation cost, supply and demand are interval grey numbers. Our method uses the concepts of center and width of grey numbers. One of the advantages of the proposed method compared to other methods that use grey number whitening is that the uncertainty in the input data is taken into account at the output of the method and it consists of five simple steps. The solution procedure is illustrated with a numerical example. Also, the new method can be served as an important tool for decision-makers when they are handling various types of logistic problems having uncertainty parameters such as grey numbers. Further, the proposed method is extended to fuzzy grey transportation problems.