  We derive the analytical time delay of light propagating in the equatorial
plane and parallel to the velocity of a moving Kerr-Newman black hole up to the
second post-Minkowskian order via integrating the null geodesic equations. The
velocity effects are expressed by a very compact form. We then concentrate on
analyzing the magnitudes of the correctional effects on the second-order
contributions to the delay and discuss their possible detection. Our result in
the first post-Minkowskian approximation is in agreement with Kopeikin and
Sch\"{a}fer's formulation which is based on the retarded Li\'{e}nard-Wiechert
potential.
