  In this work, we propose a model of Einstein--Gauss-Bonnet gravity coupled
with two scalar fields. The two scalar fields are considered to be ``frozen''
or they become non-dynamical by employing appropriate constraints in terms of
Lagrange multiplier fields. We show that, even in the case that the arbitrary
spherically symmetric spacetime is dynamical, we can construct a model where
the wormhole spacetime is a stable solution in this framework. We especially
concentrate on the model reproducing the dynamical wormhole, where the wormhole
appears in a finite-time interval. We investigate the propagation of the
gravitational wave in the wormhole spacetime background and we show that the
propagation speed is different from that of light $\to$ light in general, and
there is a difference in the speeds between the incoming propagating wave and
the outgoing propagating gravitational wave.
