  The B-decay constant $f_B$ is an important component for studying $B$-meson
decays, which can be studied through QCD sum rules. We make a detailed
discussion on $f_B$ from two sum rules, i.e. sum rules I and II, which are
derived from the conventional correlator and the correlator with chiral
currents respectively. It is found that these two sum rules are consistent with
each other. However, the sum rules II has less uncertainty sources than that of
sum rules I, and then it can be more accurate if we know the dimension-four
gluon condensate well. It is found that $f_B$ decreases with the increment of
$m_b$, and to compare with the Belle experimental data on $f_B$, both sum rules
prefer smaller pole $b$-quark mass, $m_b=4.68\pm0.07$ GeV. By varying all the
input parameters in their reasonable region and adding all the uncertainties
together in quadrature, we obtain $f_B=172^{+23}_{-25}$ MeV for sum rules I and
$f_B=214_{-34}^{+26}$ MeV for sum rules II.
