  We introduce an anomalous top quark coupling (right-handed current) into
Standard Model Lagrangian. Based on this, a more complete calculation of $b \to
s\gamma $ decay including leading log QCD corrections from $m_{top}$ to $M_W$
in addition to corrections from $M_{W}$ to $m_b$ is given. The inclusive decay
rate is found to be suppressed comparing with the case without QCD running from
$m_t$ to $M_W$ except at the time of small values of $|f_R^{tb}|$. e.g. when
$f_R^{tb}=-0.08$, it is only $1/10$ of the value given before. As $|f_R^{tb}|$
goes smaller, this contribution is an enhancement like standard model case.
  From the newly experiment of CLEO Collaboration, strict restrictions to
parameters of this top-bottom quark coupling are found.
