  The self-accelerating branch of the Dvali-Gabadadze-Porrati (DGP)
five-dimensional braneworld has provided a compelling model for the current
cosmic acceleration. Recent observations, however, have not favored it so much.
We discuss the solutions which contain a de Sitter 3-brane in the cascading DGP
braneworld model, which is a kind of higher-dimensional generalizations of the
DGP model,where a $p$-dimensional brane is placed on a $(p+1)$-dimensional one
and the $p$-brane action contains the $(p+1)$-dimensional induced scalar
curvature term. In the simplest six-dimensional model, we derive the solutions.
Our solutions can be classified into two branches, which reduce to the
self-accelerating and normal solutions in the limit of the original
five-dimensional DGP model. In the presence of the six-dimensional bulk
gravity, the `normal' branch provides a new self-accelerating solution. The
expansion rate of this new branch is generically lower than that of the
original one, which may alleviate the fine-tuning problem.
