  The loop super-Virasoro conformal superalgebra $\mathfrak{cls}$ associated
with the loop super-Virasoro algebra is constructed in the present paper. The
conformal superderivation algebra of $\mathfrak{cls}$ is completely determined,
which is shown to consist of inner superderivations. And nontrivial free and
free $\mathbb{Z}$-graded $\mathfrak{cls}$-modules of rank two are classified.
We also give a classification of irreducible free $\mathfrak{cls}$-modules of
rank two and all irreducible submodules of each free $\mathbb{Z}$-graded
$\mathfrak{cls}$-module of rank two.
