We are concerned with the breakdown of strong solutions to the three-dimensional compressible magnetohydrodynamic equations with density-dependent viscosity. It is shown that for the initial density away from vacuum, the strong solution exists globally if the gradient of the velocity satisfies $ \|\nabla{\bf{u}}\|_{L^{2}(0,T;L^\infty)}<\infty $. Our method relies upon the delicate energy estimates and elliptic estimates.
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