  We generally investigate the scalar field model with the lagrangian
$L=F(X)-V(\phi)$, which we call it {\it General Non-Canonical Scalar Field
Model}. We find that it is a special square potential(with a negative minimum)
that drives the linear field solution($\phi=\phi_0t$) while in K-essence
model(with the lagrangian $L=-V(\phi)F(X)$) the potential should be taken as an
inverse square form. Hence their cosmological evolution are totally different.
We further find that this linear field solutions are highly degenerate, and
their cosmological evolutions are actually equivalent to the divergent model
where its sound speed diverges. We also study the stability of the linear field
solution. With a simple form of $F(X)=1-\sqrt{1-2X}$ we indicate that our model
may be considered as a unified model of dark matter and dark energy. Finally we
study the case when the baryotropic index $\gamma$ is constant. It shows that,
unlike the K-essence, the detailed form of F(X) depends on the potential
$V(\phi)$. We analyze the stability of this constant $\gamma_0$ solution and
find that they are stable for $\gamma_0\leq1$. Finally we simply consider the
constant c_s^2 case and get an exact solution for F(X)
