  This paper is concerned with the Cauchy problem of the multi-dimensional
incompressible magnetohydrodynamic equations with inhomogeneous density and
fractional dissipation. It is shown that when $\alpha+\beta=1+\frac{n}{2}$
satisfying $1\leq \beta\leq \alpha\leq\min
\{\frac{3\beta}{2},\frac{n}{2},1+\frac{n}{4}\}$ and $\frac{n}{4}<\alpha$ for
$n\geq3$ , then the inhomogeneous incompressible MHD equations has a unique
global strong solution for the initial data in Sobolev space which do not need
a small condition.
