  Let $\mathfrak{g}=\mathfrak{g}_{\bar{0}}+\mathfrak{g}_{\bar{1}}$ be a basic
Lie superalgebra, $\mathcal{W}_0$ (resp.$\mathcal{W}$) be the finite
W-(resp.super-) algebras constructed from a fixed nilpotent element in
$\mathfrak{g}_{\bar{0}}$. Based on a relation between finite W-algebra
$\mathcal{W}_0$ and W-superalgebra $\mathcal{W}$ found recently by the author
and Shu, we study the finite dimensional representations of finite
W-superalgebras in this paper. We first formulate and prove a version of
Premet's conjecture for the finite W-superalgebras from basic simple Lie
superalgebras. As in the W-algebra case, the Premet's conjecture is very close
to give a classification to the finite dimensional simple
$\mathcal{W}$-modules. In the case of $\ggg$ is Lie superalgebras of basic type
\Rmnum{1}, we prove the set of simple $\mathcal{W}$-supermodules is bijective
with that of simple $\mathcal{W}_0$-modules; presenting a triangular
decomposition to the tensor product of $\mathcal{W}$ with a Clifford algebra,
we also give an algorithm to compute the character of the finite dimensional
simple $\mathcal{W}$-supermodules with integral central character.
