  We consider a cosmological model dominated by stiff fluid with a constant
bulk viscosity. We classify all the possible cases of the universe predicted by
the model and analyzing the scale factor, density as well as the curvature
scalar. We find that when the dimensionless constant bulk viscous parameter is
in the range $0 < \bar\zeta <6$ the model began with a Big Bang, and make a
transition form the decelerating expansion epoch to an accelerating epoch, then
tends to the de Sitter phase as $ t\to \infty$. The transition into the
accelerating epoch would be in the recent past, when $4<\bar\zeta<6.$ For
$\bar\zeta>6$ the model doesn't have a Big Bang and suffered an increase in the
fluid density and scalar curvature as the universe expands, which are
eventually saturates as the scale factor $a \to \infty$ in the future. We have
analyzed the model with statefinder diagnostics and find that the model is
different from $\Lambda$CDM model but approaches $\Lambda$CDM point as $a \to
\infty.$ We have also analyzed the status of the generalized second law of
thermodynamics with apparent horizon as the boundary of the universe and found
that the law is generally satisfied when $0 \leq \bar\zeta <6$ and for
$\bar\zeta >6$ the law is satisfied when the scale factor is larger than a
minimum value.
