  In this paper, we investigate the gravitational collapse to form the black
hole in the acceleratingly expanding universe in the frame of
Einstein--Gauss-Bonnet theory having two scalar fields and we study the
propagation of the gravitational wave (GW). The collapsing spacetime can be
obtained by using the formulation of the ``reconstruction'', that is, we find a
model that realises the desired or given geometry. In the reconstructed models,
ghosts often appear, which could be eliminated by imposing constraints. We show
that the standard cosmological solutions or self-gravitating objects such as a
planet, the Sun, various types of stars, etc., in Einstein's gravity, are also
solutions in this model. Using the dynamical value of Gauss-Bonnet coupling,
the propagation of the high-frequency GW is investigated. The propagating speed
changes due to the coupling during the period of the black hole formation. The
speed at which the GW propagates The speed at which the GW propagates going
into the black hole is different from that of the wave going out.
