  Since the first detection of gravitational waves, they have been used to
investigate various fundamental problems, including the variation of physical
constants. Regarding the gravitational constant, previous works focused on the
effect of the gravitational constant variation on the gravitational wave
generation. In this paper, we investigate the effect of the gravitational
constant variation on the gravitational wave propagation. The Maxwell-like
equation that describes the propagation of gravitational waves is extended in
this paper to account for situations where the gravitational constant varies.
Based on this equation, we find that the amplitude of gravitational waves will
be corrected. Consequently the estimated distance to the gravitational wave
source without considering such a correction may be biased. Applying our
correction result to the well known binary neutron star coalescence event
GW170817, we get a constraint on the variation of the gravitational constant.
Relating our result to the Yukawa deviation of gravity, we for the first time
get the constraint of the Yukawa parameters in 10Mpc scale. This scale
corresponds to a graviton mass $m_g\sim10^{-31}$eV.
