Because of the high non-ellipticity associated with intense anticyclonic flows in solving the non-linear balance (NLB) equations, few studies have been performed to investigate the three-dimensional balanced characteristics of hurricanes with inner-core asymmetries. In this study, the inner-core dynamics of hurricanes is examined by applying an NLB model to a high-resolution explicit simulation of Hurricane Andrew (1992) by Liu et al. (1997, 1999). The non-ellipticity of the NLB system is overcome by combining it with the potential vorticity (PV) equation. We first define the axisymmetric mean height field by solving the NLB equation using the azimuthally averaged tangential winds, and then obtain the axisymmetric PV from the balanced winds and heights. Since to a large extent the hurricane is symmetric, the perturbation PV, defined as a deviation from the axisymmetric PV, is one order of magnitude smaller than the axisymmetric component, the PV inversion algorithm of Davis and Emanuel (1991) is adopted to invert the three-dimensional perturbation wind and temperature distributions of the hurricane. Then, the divergent component of horizontal winds is obtained through the NLB Omega equation with incorporation of the diabatic heating and boundary-layer effects. A comparison of the inverted and simulated mass and wind fields shows that most of the three-dimensional hurricane flows are quasi-balanced, including the eyewall updrafts, the boundary-layer inflow, the upper-level outflow and descent in the eye. From the difference between the simulated and inverted fields, we find that most of the unbalanced flow is associated with transience in latent heating and the centrifugal force in the vicinity of the maximum wind. The PV inversion algorithm also allows us to isolate the contributions of the boundary layer, diabatic heating and the asymmetric disturbances to the development of vertical motion in the inner-core regions. It is found that the latent heating is a major contributor to the eyewall updrafts. The contribution of surface friction is constrained in the boundary layer. The three-dimensional balanced fields will be used to diagnose the vortex-Rossby waves in the simulated hurricane because of the absence of gravity waves in the balanced flow.