  We conduct an analysis of a $U(1)_{B-L}$ extended inert doublet model and
obtained the parameter space allowing strong first order phase transitions. We
show that a large part of the parameter space can cause double first-order
phase transitions. Whereas both of these phase transitions can generate a
detectable stochastic gravitational wave background, one of them can create
primordial black holes with appreciable abundance. The primordial black holes
generated at the high scale transition can account for the dark matter
maintaining the correct relic abundance. We also show specific benchmark cases
and their consequences from the aspect of primordial black holes and
gravitational waves.
