  The $B_c$ meson is a doubly heavy quark-antiquark bound state and carries
flavors explicitly, which provides a fruitful laboratory for testing potential
models and understanding the weak decay mechanisms for heavy flavors. In view
of the prospects in $B_c$ physics at the hadronic colliders as Tevatron and
LHC, $B_c$ physics is attracting more and more attention. It has been shown
that a high luminosity $e^+e^-$ collider running around the $Z^0$-peak is also
helpful for studying the properties of $B_c$ meson and has its own advantages.
For the purpose, we write down an event generator for simulating $B_c$ meson
production through $e^+e^-$ annihilation according to relevant publications. We
name it as BEEC, in which the color-singlet $S$-wave and $P$-wave
$(c\bar{b})$-quarkonium states together with the color-octet $S$-wave
$(c\bar{b})$-quarkonium states can be generated. BEEC can also be adopted to
generate the similar charmonium and bottomnium states via the semi-exclusive
channels $e^{+}+e^{-}\rightarrow |(Q\bar{Q})[n]\rangle +Q +\bar{Q}$ with $Q=b$
and $c$ respectively. To increase the simulation efficiency, we simplify the
amplitude as compact as possible by using the improved trace technology. BEEC
is a Fortran programme written in a PYTHIA-compatible format and is written in
a modularization structure, one may apply it to various situations or
experimental environments conveniently by using the GNU C compiler {\bf make}.
A method to improve the efficiency of generating unweighted events within
PYTHIA environment has been suggested. Moreover, BEEC will generate a standard
Les Houches Event data file that contains useful information of the meson and
its accompanying partons, which can be conveniently imported into PYTHIA to do
further hadronization and decay simulation.
