  In this paper, we determine upper bound for the non-abelian tensor product of
finite dimensional Lie superalgebra. More precisely, if $L$ is a non-abelian
nilpotent Lie superalgebra of dimension $(k \mid l)$ and its derived subalgebra
has dimension $(r \mid s)$, then $ \dim (L\otimes L) \leq
(k+l-(r+s))(k+l-1)+2$. We discuss the conditions when the equality holds for
$r=1, s=0$ explicitly.
