  The detection of gravitational wave (GW) has opened a new window to test the
theory of gravity in the strong field regime. In general relativity (GR), GW
can only possess two tensor polarization modes, which are known as the $+$ and
$\times$ modes. However, vector and scalar modes can exist in some modified
theories of gravity, and we can test the gravitational theories by probing
these extra polarization modes. As a space-borne GW detector, TianQin will be
launched in the 2030s, and it is expected to observe plenty of GW signals,
including those from nearly ten-thousands double white dwarfs (DWDs) in our
galaxy. This offers an excellent chance for testing the existence of extra
polarization modes. In this article, we analyze the capability of detecting the
extra polarization modes with DWDs. For the extra modes, we consider both the
leading order dipole radiation and the subleading quadrupole radiation. We find
that the capability of TianQin has very strong dependency on the source
orientation. We also analyze all the verification binaries with determined
position and frequency, and find that ZTF J1539 can give the best constraint on
the extra polarization modes. We have also considered the case of TianQin twin
constellation, and the joint observation with LISA.
