Abstract: It is shown a solution to the stability of the fast approximation for network flow optimization.By our method,the minimal cost flow computation can be ensured for O(k(ε-2+lgk)lgn) separate flows.Consequently,approximate solution can be obtained for the maximum-concurrent flow and it can be ensured to be optimal.In our method,the related parameters can be roughly intepreted as follows:k means the number of concurrent commodies,n is the number of nodes,and ε is the desired precision.