  We propose a variable Eddington factor, depending on the {\it flow velocity}
$v$, for the relativistic radiative flow, whose velocity becomes of the order
of the speed of light. When the gaseous flow is radiatively accelerated up to
the relativistic regime, the velocity gradient becomes very large in the
direction of the flow. As a result, the radiative diffusion may become {\it
anisotropic} in the comoving frame of the gas. Hence, in a flow that is
accelerated from subrelativistic to relativistic regimes, the Eddington factor
should be different from 1/3 even in the diffusion limit. As a simple form, the
velocity-dependent Eddington factor may be written as $f(\beta) =
1/3+(2/3)\beta$, where $\beta=v/c$. Using the velocity-dependent Eddington
factor, we can solve the rigorous equations of the relativistic radiative flow
accelerated up to the relativistic speed. We also propose a generalized form
for a variable Eddington factor as a function of the optical depth $\tau$ as
well as the flow velocity: %$f(\tau, \beta) = {1/3} + {2/3} %
\frac{1+(\tau+1)\beta}{1+\tau+\beta}$ $f(\tau, \beta) = 1/3 + (2/3)
[{1+(\tau+1)\beta}]/({1+\tau+\beta})$ for a spherically symmetric case. The
velocity-dependent Eddington factor can be used in various relativistic
radiatively-driven flows, such as black-hole accretion flows, relativistic
astrophysical jets and outflows, and relativistic explosions like gamma-ray
bursts.
