In this paper, we consider the Dirichlet problem of three-dimensional inhomogeneous incompressible micropolar equations with density-dependent viscosity. Under the assumption that the coefficients are power functions of the density, we establish the global existence of strong solutions as long as the initial density is linearly equivalent to a large constant state. There is no restriction on the size of the initial velocity and micro-rotational velocity. As a byproduct, we prove the exponential decay for the solution.