  General Relativity predicts only two tensor polarization modes for
gravitational waves while at most six possible polarization modes are allowed
in general metric theory of gravity. The number of polarization modes is
determined by the specific modified theory of gravity. Therefore, the
determination of polarization modes can be used to test gravitational theory.
We introduce a concrete data analysis pipeline for a space-based detector such
as LISA to detect the polarization modes of gravitational waves. This method
can be used for monochromatic gravitational waves emitted from any compact
binary system with known sky position and frequency to detect mixtures of
tensor and extra polarization modes. We use the source J0806.3+1527 with
one-year simulation data as an example to show that this approach is capable of
probing pure and mixed polarizations without knowing the exact polarization
modes. We also find that the ability of detection of extra polarization depends
on the gravitational wave source location and the amplitude of non-tensorial
components.
