  Space-based gravitational-wave detectors consist of a triangle of three
spacecraft, which makes it possible to detect polarization modes of
gravitational waves due to the motion of the detectors in space. In this paper
we explore the ability of Taiji to detect the polarization modes in the
parametrized post-Einsteinian framework. Assuming massive black hole binaries
with the total mass of $M=4\times10^5\,M_{\odot}$ at redshift of $z=1$, we find
that Taiji can measure the dipole and quadruple emission
($\Delta\alpha_D/\alpha_D$ and $\Delta\alpha_Q/\alpha_Q$) with the accuracy of
up to $\sim 0.04\%$, with the fiducial value of $\alpha_D=0.001$, the scalar
transverse and longitudinal modes ($\Delta\alpha_B$ and $\Delta\alpha_L$) up to
$\sim 0.01$, and the vector modes ($\Delta\alpha_V$) up to $\sim 0.0005$.
