Large-eddy simulation (LES) of the turbulent duct flows in a liquid metal magnethydrodynamic (MHD) power generator is examined to reveal the behavior of the MHD flows and the turbulent structures. The non-uniform magnetic flux density in the streamwise direction produces two eddy currents. The eddy current causes the wall-jet flows with M-shaped mean streamwise velocity profiles in the plane perpendicular to the external magnetic field. In contrast, the Hartmann flows with the flattened velocity profiles by the Lorentz force are produced in the plane parallel to the external magnetic field. In the case of the strong magnetic flux density, the turbulence structure similar to the Karman vortex sheets emerge in the downstream duct. As for the secondary flows, two vortexes at the corner of the duct disappear with applied magnetic flux density. When the magnetic field is applied, the frequency spectrum of the Reynolds stress gives the strong intensity in a low frequency regime.