  In this paper, we are concerned with the global well-posedness of 3D
inhomogeneous incompressible Navier-Stokes equations with density-dependent
viscosity when the initial velocity is sufficiently small in the critical Besov
space $\dot{B}^{\frac 12}$. Compared with the previous result of Abidi and
Zhang (Science China Mathematics 58 (6) (2015) 1129-1150), we remove the
smallness assumption of the viscosity $\mu(\rho_0)-1$ in $L^{\infty}$-norm.
