  We study the cohomology of Lie superalgebra of vector fields on affine
super-spaces $\mathbb{A}^{m,n}$ with trivial coefficients. Previously known
results covered the classical case $\mathbb{A}^m = \mathbb{A}^{m,0}$ as well as
the case $\mathbb{A}^{m,n}$ with $m \leq n$. In this paper we perform the
computation for super-spaces $\mathbb{A}^{m,1}$.
