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 $Λ$ 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 $Λ=0$ as a special case and it discriminate from the standard $Λ$-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 $ω=-1$ both from above and below, but the crossing does not occur. It predicts present value of $ω\sim -1\mp 0.07$, 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.

9 pages