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In this paper, we consider the stability problem on perturbation near a physically steady state solution of the 3D generalized incompressible magnetohydrodynamic system in Lei-Lin space. The global stability and analytic estimates for small perturbation are established by the semigroup method in the critical space χ 1 - 2 α (R 3) with 1 2 ≤ α ≤ 1 , where linear terms from perturbation incur much difficulty. By introducing a diagonalization process we successfully eliminate the linear terms. Then, by virtue of the analytic estimates for a solution, the temporal decay rate (1 + t) - (5 4 α - 1) of the global solution is obtained. [ABSTRACT FROM AUTHOR]