The mechanism by which the Earth and other planets maintain their magnetic fields against ohmic decay is among the longest standing problems in planetary science. Although it is widely acknowledged that these fields are maintained by dynamo action, the mechanism by which the dynamo operates is in large part not understood. Numerical simulations of the dynamo process in the Earth’s core(1-4) have produced magnetic fields that resemble the Earth’s field, but it is unclear whether these models accurately represent the extremely low values of viscosity believed to be appropriate to the core. Here we describe the results of a numerical investigation of the dynamo process that adopts an alternative approach(5) to this problem in which, through the judicious choice of boundary conditions, the effects of viscosity are rendered unimportant. We thereby obtain a solution that at leading order operates in an Earth-like dynamical regime. The morphology and evolution of the magnetic field and the fluid flow at the tore-mantle boundary are similar to those of the Earth, and the field within the core is qualitatively similar to that proposed on theoretical grounds(6).