  In this paper, we study the Cauchy problem of the isentropic compressible
magnetohydrodynamic equations in $\mathbb{R}^{3}$. When
$(\gamma-1)^{\frac{1}{6}}E_{0}^{\frac{1}{2}}$, together with the
$\|H_{0}\|_{L^{2}}$, is suitably small, a result on the existence of global
classical solutions is obtained. It should be pointed out that the initial
energy $E_{0}$ except the $L^{2}$- norm of $H_{0}$ can be large as $\gamma$
goes to 1, and that throughout the proof of the theorem in the present paper,
we make no restriction upon the initial data $(\rho_{0},u_{0})$. Our result
improves the one established by Li-Xu-Zhang in \cite{H.L. L}, where, with small
initial engergy, the existence of classical solution was proved.
