  We introduce a novel representation of Virasoro algebra in open string field
theory. Elements of the algebra are vector fields on the $K$-space, where $K$
is the string field that generates a world sheet strip in sliver frame. The
generators introduce a global symmetry of open string field theory. We also
derive a representation of Virasoro algebra for nontrivial open string
background described by the formal pure gauge solution. Generators for 0, 1 and
2 D-branes are explicitly studied and different behaviors around $K=0$ are
observed.
