  We study the spectrum of gravitational perturbations about a vacuum de Sitter
brane with the induced 4D Einstein-Hilbert term, in a 5D Minkowski spacetime
(DGP model). We consider solutions that include a self-accelerating univese,
where the accelerating expansion of the universe is realized without
introducing a cosmological constant on the brane. The mass of the discrete mode
for the spin-2 graviton is calculated for various $Hr_c$, where $H$ is the
Hubble parameter and $r_c$ is the cross-over scale determined by the ratio
between the 5D Newton constant and the 4D Newton constant. We show that, if we
introduce a positive cosmological constant on the brane ($Hr_c >1$), the spin-2
graviton has mass in the range $0 < m^2 < 2H^2$ and there is a normalisable
brane fluctuation mode with mass $m^2=2 H^2$. Although the brane fluctuation
mode is healthy, the spin-2 graviton has a helicity-0 excitation that is a
ghost. If we allow a negative cosmological constant on the brane, the brane
bending mode becomes a ghost for $1/2 < Hr_c <1$. This confirms the results
obtained by the boundary effective action that there exists a scalar ghost mode
for $Hr_c >1/2$. In a self-accelerating universe $Hr_c=1$, the spin-2 graviton
has mass $m^2=2H^2$, which is known to be a special case for massive gravitons
in de Sitter spacetime where the graviton has no helicity-0 excitation and so
no ghost. However, in DGP model, there exists a brane fluctuation mode with the
same mass and there arises a mixing between the brane fluctuation mode and the
spin-2 graviton. We argue that this mixing presumably gives a ghost in the
self-accelerating universe by continuity across $Hr_c=1$, although a careful
calculation of the effective action is required to verify this rigorously.
