Constraint on the mass of graviton with gravitational waves

We consider the effects of the mass of graviton on both the waveform of gravitational waves and the antenna response to gravitational waves. We find the effect on the response function is negligible for small mass. By using the Fisher matrix method, we make parameter estimations with space-based gravitational wave detectors for massive black hole binaries in massive gravity theory. The wavelength of massive graviton is constrained to be $λ_g\gtrsim 10^{17}$ m and the mass is constrained to be $m_g\lesssim 10^{-60}$ kg by one year's observation of massive black hole binaries with space-based gravitational wave detectors.