  Gravitational-wave data can be used to test general relativity in the
extreme, highly nonlinear, and strong-field regime. Modified gravity theories
such as Einstein-dilation-Gauss-Bonnet and dynamical Chern-Simons gravity are
supposed to be well checked with some specific signals. We analyze
gravitational-wave data from the first half of the third observing run of
Advanced LIGO/Virgo to place constraints on the parameters of these two
theories. The dynamical Chern-Simons gravity remains unconstrained. While for
the Einstein-dilation-Gauss-Bonnet gravity, we have $\sqrt{\alpha_{\rm
EdGB}}\lesssim 0.40\,\rm km$ with the data of GW190814 and $\sqrt{\alpha_{\rm
EdGB}}\lesssim 0.24\,\rm km$ if GW190425 is a neutron star$-$black hole merger
event, as allowed by the current observations. Such constraints are improved by
a factor of $\sim 10-20$ in comparison to that set by the GWTC-1 events. We
also demonstrate that the Bayes approach is more effective than the reweight
method to constrain the Einstein-dilation-Gauss-Bonnet model.
