According to the wide use of integer programming in many fields, affords toward finding and solving sub classes of these problems which are solvable in polynomial time seems to be important and useful. Integer linear programming (ILP) problems have the general form: Min {CT x: Ax= b, x≥ 0, x∈ Zn} where Zn is the set of n-dimensional integer vectors. Algorithmic solution of ILP is at great interest, in this paper we have presented a polynomial algorithm for a special case of the ILP problems; we have used a graph theoretical formulation of the problem which leads to an O [mn (m+ n)] solution where m and n are dimensions of coefficient matrix X.