  In this work, we propose a new source for gravitational wave (GW) radiation
associated with the quantum chromodynamics (QCD) phase transition in the inner
cores of neutron stars. The mechanism is based on the bubble dynamics during
the first-order phase transition from nuclear matter to quark matter. We
identify the characteristic frequency to be of order $\omega_c\sim 10^6~{\rm
rad/s}$ for this kind of sources and the strain magnitude ($h\sim 10^{-24}$ for
a neutron star at a distance of $0.1~{\rm Mpc}$) reachable by future GW
detectors. The GW spectra are shown to be useful to check the transition nature
at high baryon chemical potential as well as to constrain the radius and
density of the inner cores, which are still indistinct up to now.
