Parity-violating (PV) gravity has recently attracted interest in several aspects. One of them is the axion-graviton coupling to test axion-dark matter model. Moreover, by extending Chern-Simons (CS) gravity to include derivatives of a scalar field up to second order, a more general class of PV gravity theory, which we call the CNCL model, has been proposed~[M. Crisostomi et al., Phys. Rev. D, 97, 044034 (2018)]. The model can be further extended by including even higher derivatives of the scalar field and/or higher curvature terms. In this paper, we discuss the effect of parity violation in gravitational sector on the propagation of gravitational waves from binary coalescence by introducing a model-independent parametrization of modification. Our parametrization includes the CNCL model as well as CS gravity. The effect of parity violation on the gravitational waveform is maximum when the source binary orientation to our line of sight is edge-on, while the modified waveform reduces to the parity-symmetric one when the source is face-on. We perform a search for the signature of such modification by using LIGO/Virgo O1/O2 catalog. We find that the catalog data is consistent with general relativity and obtain constraints on parity violation in gravity for various post-Newtonian order modifications for the first time. The obtained constraint on CS gravity is consistent with the results in previous works. On the other hand, the constraint on the CNCL model that we obtain is tighter than the previous results by roughly 7 orders of magnitude.