In　this　paper,　we　are　interested　in　the　global　well-posedness　of　the　strong　solutions　to　the　Cauchy　problem　on　the　compressible　magnetohydrodynamics　system　with　Hall　effect.　Moreover,　we　establish　the　convergence　rates　of　the　above　solutions　trending　towards　the　constant　equilibrium　(&　rho;　over　bar　,0,B　over　bar　)\documentclass[12pt]{minimal}\usepackage{amsmath}\usepackage{wasysym}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{amsbsy}\usepackage{mathrsfs}\usepackage{upgreek}\setlength{\oddsidemargin}{-69pt}\begin{document}$$({\bar{\rho　}},0,\bar{\textbf{B}})$$\end{document},　provided　that　the　initial　perturbation　belonging　to　H3(R3)&　AND;B2,&　INFIN;-s(R3)\documentclass[12pt]{minimal}\usepackage{amsmath}\usepackage{wasysym}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{amsbsy}\usepackage{mathrsfs}\usepackage{upgreek}\setlength{\oddsidemargin}{-69pt}\begin{document}$$H＜^＞3({\mathbb　{R}}＜^＞3)　\cap　B_{2,　\infty　}＜^＞{-s}({\mathbb　{R}}＜^＞3)$$\end{document}　for　s　&　ISIN;(0,32]\documentclass[12pt]{minimal}\usepackage{amsmath}\usepackage{wasysym}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{amsbsy}\usepackage{mathrsfs}\usepackage{upgreek}\setlength{\oddsidemargin}{-69pt}\begin{document}$$s　\in　(0,\frac{3}{2}]$$\end{document}　is　sufficiently　small.