  For a K3 surface X and its bounded derived category of coherent sheaves D(X),
we have the notion of stability conditions on D(X) in the sense of
T.Bridgeland. In this paper, we show that the moduli stack of semistable
objects in D(X) with a fixed numerical class and a phase is represented by an
Artin stack of finite type over C. Then following D.Joyce's work, we introduce
the invariants counting semistable objects in D(X), and show that the
invariants are independent of a choice of a stability condition.
