  The standard model extension (SME) is an effective field theory framework
that can be used to study the possible violations of Lorentz symmetry in the
gravitational interaction. In the SME's gauge invariant linearized gravity
sector, the dispersion relation of GWs is modified, resulting in anisotropy,
birefringence, and dispersion effects in the propagation of GWs. In this paper,
we mainly focus on the non-birefringent and anisotropic dispersion relation in
the propagation of GWs due to the violation of Lorentz symmetry. With the
modified dispersion relation, we calculate the corresponding modified waveform
of GWs generated by the coalescence of compact binaries. We consider the
effects from the operators with the lowest mass dimension $d=6$ in the gauge
invariant linearized gravity sector of the SME which are expected to have the
dominant Lorentz-violating effect on the propagation of GWs. For this case, the
Lorentz-violating effects are presented by 25 coefficients and we constrain
them independently by the ``maximal-reach" approach. We use 90 high-confidence
GW events in the GWTC-3 catalog and use {\tt Bilby}, an open source software,
and {\tt Dynest}, a nested sampling package, to perform parameter estimation
with the modified waveform. We do not find any evidence of Lorentz violation in
the GWs data and give a $90\%$ confidence interval for each Lorentz violating
coefficient.
