  In this paper the accelerating expansion of our universe at the late cosmic
evolution time in a generally modified (extended) \emph{Chaplygin gas} (Dark
Fluid) model is detailed, which is characterized by two parameters ($m$,
$\alpha$). Different choices to the parameters $m$ and $\alpha$ divide this
model into two main kinds of situation by different properties with
cosmological interests. With proper choices of parameters, we find that this
extended model can realize the phantom divide $w=-1$ (Equation Of State
parameter) crossing phenomenon with interesting ranges of the scale factor
value $a(t)$ corresponding to $w=-1$ and present value of state parameter $w$.
  Additionally, through Taylor series expansion of the function $A(a)$ in the
extended Chaplygin gas model, a specific Equation of State is gained. Under the
framework of Friedman-Robertson-Walker cosmic model, it can successfully
explain the accelerating expansion of our universe. However, the value of $w$
in this case is large than -1, that is, indicating it like a quintessence fluid
and no $w=-1$ crossing occurs.
