  We investigate the single transverse-spin asymmetry with a $\sin
(2\phi-\phi_S)$ modulation in the pion-induced Drell-Yan process within the
theoretical framework of the transverse momentum dependent factorization. The
asymmetry is contributed by the convolution of the Boer-Mulders function and
the transversity. We adopt the model results for the distributions of the pion
meson from the light-cone wavefunction approach and the available
parametrization for the distributions of the proton to numerically estimate the
$\sin (2\phi-\phi_S)$ asymmetry in $\pi^- p$ Drell-Yan at the kinematics of the
COMPASS at CERN. To implement the TMD evolution formalism of parton
distribution functions, we apply the recently extracted nonperturbative Sudakov
form factor associated with the distribution functions of the proton and the
pion. It is found that our prediction on the single transverse-spin dependent
asymmetry ${\sin (2\phi-\phi_S)}$ as functions of $x_p$, $x_\pi$, $x_F$ and
$q_\perp$ is qualitatively consistent with the recent COMPASS measurement in
both sign and magnitude.
