  In a paper by Su and Zhao, the Lie algebra $A[D]=A\otimes F[D]$ of Weyl type
was defined and studied, where $A$ is a commutative associative algebra with an
identity element over a field $F$ of arbitrary characteristic, and $F[D]$ is
the polynomial algebra of a commutative derivation subalgebra $D$ of $A$. The
2-cocycles of a class of $A[D]$ were determined by Su. In the present paper, we
determine the 2-cocycles of a class of Lie superalgebras of Weyl type over a
field $F$ of characteristic 0.
