In the existing deterministic network, the capacity of each arc has determined property. But actually, it may be a property which cannot be determined. Even though it should be determining, it contains many errors. In treating these kinds of problems, fuzzy theory is suitable. Recently, due to development the study on complicated and indefinited systems which contain fuzziness could be possible. This paper includes that the capacity of each arc and the goal quantity with nonnegative integer have the fuzziness. The object is to search the new mathod of fuzzy maximal flow quantity. If the degree of arc membership function of the minimal cut part is not larger than that of arc membership function of the part except the minimal cut, first calcurate nonfuzzy maximal flow quantity, and then can compute the optimal quantity the 3rd step at one time with Max-Min fuzzy operating in the arc capacity of minimal cut and the goal quantity without a great number of recalculation.