Inspired by the analogy between the magnetic field and velocity fieldof incompressible fluid flow, we propose a fluid dynamics approach for comput-ing nonlinear force-free magnetic fields. This method has the advantage that thedivergence-free condition is automatically satisfied, which is a sticky issue for manyother algorithms, and we can take advantage of modern high resolution algorithmsto process the force-free magnetic field. Several tests have been made based on thewell-known analytic solution proposed by Low & Lou. The numerical results arein satisfactory agreement with the analytic ones. It is suggested that the newlyproposed method is promising in extrapolating the active region or the whole sunmagnetic fields in the solar atmosphere based on the observed vector magnetic fieldon the photosphere.