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We study gravitational waves in the presence of the string axion dark matter and the gravitational Chern-Simons coupling. We show that the parametric resonance of gravitational waves occurs due to the axion coherent oscillation and the circular polarization of gravitational waves is induced by the Chern-Simons coupling. For example, the gravitational waves should be enhanced ten times every $10^{−8}$ pc in the presence of the axion dark matter with mass $10^{−10}$ eV provided the coupling constant $\ell = 10^8$ km. After 10 kpc propagation, the amplitude of GWs are enhanced by 10^10^12 and the polarization of GWs becomes completely circular. However, we have never observed these signatures. This indicates that the Chern-Simons coupling constant and/or the abundance of the light string axion should be strongly constrained than the current limits $\ell ≤ 10^{8}$ km and $\rho ≤ 0.3$ GeV/cm^3. -References: [1] DY and Jiro Soda, "Exploring the string axiverse and parity violation in gravity with gravitational waves", Int. J. Mod. Phys. D [2] Jiro Soda and DY, "Exploring String Axions with Gravitational Waves", Galaxies 2017, 5(4), 96

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