  In this paper, we calculate the decay rate and CP asymmetry of the $B_s \to
\pi^+\pi^-$ decay in perturbative QCD approach with Sudakov resummation. Since
none of the quarks in final states is the same as those of the initial $B_s$
meson, this decay can occur only via annihilation diagrams in the standard
model. Besides the current-current operators, the contributions from the QCD
and electroweak penguin operators are also taken into account. We find that (a)
the branching ratio is about $4 \times 10^{-7}$; (b) the penguin diagrams
dominate the total contribution; and (c) the direct CP asymmetry is small in
size: no more than $3% $; but the mixing-induced CP asymmetry can be as large
as ten percent testable in the near future LHC-b experiments.
