  We study the polarization modes of gravitational waves in general
Einstein-vector theory with an arbitrary constant background vector field under
a Minkowski background. We compare these polarization modes with those of other
vector-tensor theories and constrain the parameter spaces based on the
gravitational-wave event GW170817 with its electromagnetic counterpart
GRB170817A and observations of pulsar timing arrays. The presence of the
background vector field leads to the anisotropy of space and a rich variety of
gravitational waves contents. Our results reveal that the polarization modes of
gravitational waves depend on the parameter spaces. There are at least two and
at most five independent polarization modes in one parameter space. In
different parameter spaces, some mixture modes are allowed, including
tensor-vector, tensor-scalar, tensor-vector-scalar, vector-scalar, and
scalar-scalar mixture modes, as well as five independent modes (excluding
$P_l$): $P_+$, $P_{\times}$, $P_x$, $P_y$, and $P_b$. In all regions of the
parameter spaces, there are always two tensor modes, which can be either
independent of or mixed with other modes. The independent $P_b$ mode
consistently exhibits the same speed as light. If the speed of tensorial
gravitational waves strictly equals that of light, only the $P_+$,
$P_{\times}$, and $P_b$ modes are permitted. Furthermore, through comparisons
of some vector-tensor theories and based on the observations of gravitational
waves, the $P_b$ mode is expected to be allowed.
