In The paper [1] represents the construction of free medial semi group through commutative semi group. In this project the structure of distributive semi group [2], [3], [4] and the commutative semi group are been used for constructing one distributive semi group through commutative semi group. The first part explains the distributive semi groups and commutative semi groups, represents the conditions that the commutative semi group should complete whereof to construct distributive semi group. The second part contains the contruction of the free distributive semi group using indications of the first part. Pointing that in this project I will try the same technique to accompany the different semi groups.