  QCD corrections to the penguin induced charmless inclusive $B$ decays are
performed to an improved leading-log approximation. For process $b \to s
q\overline{q} $ (q=uds) and $ b \overline{q} \to s \overline{q} $, four
previous missed 4-quark operators are included to make a complete leading log
QCD corrected result. Furthermore, part of the next-leading log effect was also
given for the above processes and process $b \to s g$. In comparison to
previous QCD corrected calculations by Grigjanis et al., the inclusive decay
rates for process $b \to s q\overline{q} $ (q=ud), $b\to s s\overline{s}$ and $
b \overline{q} \to s \overline{q} $ are suppressed 10\%, 14\% and 18\%
respectively. The branching ratio of process $b \to s g$ is enhanced by 2-3
orders, the result for this process is in agreement with the result of Ciuchini
et al.
