Observations of nearly zero toroidal current in the central region of tokamaks (the "current hole") raises the question of the existence of toroidal equilibria with very low or reversed current in the core. The solutions of the Grad-Shafranov equilibrium equation with hollow toroidal current density profile including negative current density in the plasma center are investigated. Solutions of the corresponding eigenvalue problem provide simple examples of such equilibrium configurations. More realistic equilibria with toroidal current density reversal are computed using a new equilibrium problem formulation and computational algorithm which do not assume nested magnetic surfaces.