We introduce an anomalous top quark coupling (right-handed current) into the standard model Lagrangian. Based on this, a more complete calculation of b\ensuremath{\rightarrow}s\ensuremath{\gamma} decay including leading log QCD corrections from ${\mathit{m}}_{\mathit{t}}$ to ${\mathit{M}}_{\mathit{W}}$ in addition to corrections from ${\mathit{M}}_{\mathit{W}}$ to ${\mathit{m}}_{\mathit{b}}$ is given. The inclusive decay rate is found to be suppressed compared with the case without QCD running from ${\mathit{m}}_{\mathit{t}}$ to ${\mathit{M}}_{\mathit{W}}$ except at the time of small values of \ensuremath{\Vert}${\mathit{f}}_{\mathit{R}}^{\mathit{t}\mathit{b}}$\ensuremath{\Vert}. For example, when ${\mathit{f}}_{\mathit{R}}^{\mathit{t}\mathit{b}}$=-0.08, it is only 1/10 of the value given before. As \ensuremath{\Vert}${\mathit{f}}_{\mathit{R}}^{\mathit{t}\mathit{b}}$\ensuremath{\Vert} gets smaller, this contribution is an enhancement as in the standard model case. From the new experiment of the CLEO Collaboration, strict restrictions to parameters of this top-bottom quark coupling are found.