In this paper we study the closed subsemigroups of a Clifford semigroup. It is shown that{∪}Gα | Y′ ∈ P (Y ) is the set of all closed subsemigroups ofα∈Y′a Clifford semigroup S = [Y;Gα;?α,β], where Y′ denotes the subsemilattice of Y generated by Y′. In particular, G is the only closed subsemigroup of itself for a group G and each one of subsemilattices of a semilattice is closed. Also, it is shown that the semiring P (S ) is isomorphic to the semiring P (Y ) for a Clifford semigroup S=[Y;Gα;?α,β].