Antihydrogen formation in the laser-assisted positron-antiproton (nonr
elativistic) radiative recombination is investigated. The state of inc
ident positron is given by the Coulomb-Volkov wave function. The pertu
rbative dressed wave function of the atom is obtained in the soft-phot
on approximation. Our calculation shows that for a geometry of laser p
olarization parallel to the incident direction, the formation cross se
ction of antihydrogen is greatly reduced. Especially at high impact en
ergy, the reduction is remarkable.