  The uncertainties in estimating the hadronic production of the $B_c$ meson
are studied under the framework of the complete $\alpha_s^4$ approach of the
perturbative QCD and the gluon-gluon fusion mechanism. Quantitative comparisons
on the production at TEVATRON and LHC are made. Considering the detectors at
TEVATRON and LHC, we have also estimated the production with proper kinematic
cuts. Based on the results, we conclude that the experimental studies of the
$B_c$ meson at the two colliders will be complimentary and stimulative. We find
that as c.m. energy is increasing from RUN-I to RUN-II at TEVATRON, the
production cross-section increases about 20%.
