  Let $QF(S)$ be the quasifuchsian space of a closed surface $S$ of genus
$g\geq 2$. We construct a new mapping class group invariant K\"ahler metric on
$QF(S)$. It is an extension of the Weil-Petersson metric onthe Teichm\"uller
space $\mathcal T(S)\subset QF(S)$. We also calculate its curvature and prove
some negativity for the curvature along the tautological directions.
