  Within the framework of the perturbative QCD approach, we calculate the
time-like $B_cB_c(B_c^*)$ form factors $F(Q^2)$ and $A_2(Q^2)$. We include
relativistic corrections and QCD corrections, either of which can give about
$20\%$ correction to the leading-order contribution, but there are cancellation
effects between them. We calculate the cross sections of the $e^+e^-\to
B_c^-B_c^+(B_c^{*+})$ processes. The cross sections are enhanced at the $Z$
pole to be $\sigma^{PP}(Q=m_Z) \sim 1.3\times10^{-5}\text{pb}$ and
$\sigma^{PV}(Q=m_Z) \sim 2.5\times10^{-5}\text{pb}$, which are still too small
to be detected by proposed $e^+e^-$ colliders such as the Circular Electron
Positron Collider.
