  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
$\lambda_g\gtrsim 10^{17}$ 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.
