  Relativistic corrections to the pair $B_c$-meson production in
$e^+e^-$-annihilation are calculated. We investigate a production of pair
pseudoscalar, vector and pseudoscalar+vector $B_c$-mesons in the leading order
perturbative quantum chromodynamics and relativistic quark model. Relativistic
expressions of the pair production cross sections are obtained. Their numerical
evaluation shows that relativistic effects in the production amplitudes and
bound state wave functions three times reduce nonrelativistic results at the
center-of-mass energy s=22 GeV.
