  We consider a cosmology with a non-compact nonlinear sigma model.The target
space is of de-Sitter type and four scalar fields are introduced.The potential
is absent but cosmological constant term $\Lambda$ is added. One of the scalar
fields is time dependent and the remaining three fields have no time dependence
but only spatial dependence. We show that a very simple ansatz for the scalar
fields results in the accelerating universe with an exponential expansion at
late times. It is pointed out that the presence of the energy density and
pressure coming from the spatial variation of the three scalar fields plays an
essential role in our analysis which includes $\Lambda=0$ as a special case and
it discriminate from the standard $\Lambda$-dominated acceleration. We perform
a stability analysis of the solutions and find that some solutions are
classically stable and attractor. We also present a non-perturbative solution
which asymptotically approaches an exponential acceleration and discusspossible
cosmological implications in relation with dark energy. It turns out that the
equation of state approaches asymptotically $\omega =-1$ both from above and
below, but the crossing does not occur. It predicts present value of
$\omega\sim -1\mp 0.07$, which is within the region allowed by the oservational
data. This solution also exhibits a power law expansion at early times, and the
energy density of the scalar fields mimics that of the stiff matter.
