  In this work, we present a non-GR full waveform for general parametrization
of axisymmetric black holes by extending our previous PSI model. Our model
comprises two main components: an inspiral part obtained by using
phenomenological method in frequency-domain and a ringdown part derived from
quasinormal modes associated with photon motion. For quantitatively revealing
the influence of the deviation from Kerr black holes on the waveforms, we
specify our model to the bumpy black holes, which are typical examples of
non-GR black holes. The results show that the deviation from the Kerr
quadrupole moment could be measured in a high accuracy. The new waveform model
can be directly used to test black holes for the LIGO-Virgo-KAGRA observations,
the third generation detectors and space-borne interferometers.
