  We find a cosmological solution corresponding to compactification of 10d
supergravity on a warped conifold that easily circumvents `no-go' theorem given
for a warped/flux compactification, providing new perspectives for the study of
supergravity or superstring theory in cosmological backgrounds. With fixed
volume moduli of the internal space, the model can explain a physical universe
undergoing an accelerated expansion in the 4d Einstein frame, for a
sufficiently long time. The solution found in the limit that the warp factor
dependent on the radial coordinate $y$ is extremized (giving a constant
warping) is smooth and it supports a flat four-dimensional
Friedmann-Robertson-Walker cosmology undergoing a period of accelerated
expansion with slowly rolling or stabilized volume moduli.
