  By using BPS closed string, the entropy is calculated of the extremal five
dimensional black hole consisting of Dirichlet onebranes, Dirichlet fivebranes
and Kaluza-Klein momentum in the flat background approximation. In our
formulations we consider two kinds of BPS closed strings with or without a
winding number. In the former case heavy excitation modes of closed strings are
used to derive the entropy. In the latter case we have no oscillator modes and
consider collective motion of such massless closed strings. The entropy is
given by the number of the ways how we divide the Kaluza-Klein momentum among
the massless closed strings. In both cases the black hole entropy is the same
as the Bekenstein-Hawking entropy. We argue that the collective modes of closed
strings without winding is equivalent to a single closed string with winding.
We propose that the two closed string pictures are connected with the open
string pictures by the modular transformation.
