Abstract: In ,the author observed a class of transformation semigroups,namely T E(X)=f∈T X:(a,b)∈E,(f(a),f(b))∈E,where E is an equivalence on the set X.If X carries the topology generated by the basis consisting of all E classes.then T E(X) is exactly the semigroup of all continuous selfmaps of the space X.In this paper,Green's relations on T E(X) are consided and completely characterized in the case that X is finite and E is simple.