  Fix a positive integer number $r$. A class of $r$-dim Lie conformal
superalgebras named $r$-dim $i$-linear Lie conformal superalgebras are studied
for $1\leq i \leq r$. We present an equivalent characterization of this class
of Lie conformal superalgebras in $r$ dimension. Moreover, by this equivalent
characterization, several constructions and examples are given.
