  The aim of this paper is to introduce a polynomial invariant $f_K(t)$ for
virtual knots. We show that $f_K(t)$ can be used to distinguish some virtual
knot from its inverse and mirror image. The behavior of $f_K(t)$ under
connected sum is also given. Finally we discuss which kind of polynomial can be
realized as $f_K(t)$ for some virtual knot $K$.
