  In this work, we investigate the spectra of gravitational waves produced by
chiral symmetry breaking in dark quantum chromodynamics (dQCD) sector. The dark
pion ($\pi$) can be a dark matter candidate as weakly interacting massive
particle (WIMP) or strongly interacting massive particle (SIMP). For a WIMP
scenario, we introduce the dQCD sector coupled to the standard model (SM)
sector with classical scale invariance and investigate the annihilation process
of the dark pion via the $2\pi \to 2\,\text{SM}$ process. For a SIMP scenario,
we investigate the $3\pi \to 2\pi$ annihilation process of the dark pion as a
SIMP using chiral perturbation theory. We find that in the WIMP scenario the
gravitational wave background spectra can be observed by future space
gravitational wave antennas. On the other hand, when the dark pion is the SIMP
dark matter with the constraints for the chiral perturbative limit and
pion-pion scattering cross section, the chiral phase transition becomes
crossover and then the gravitational waves are not produced.
