Turbulent Taylor-Couette (TC) flow of liquid metal in the axial magnetic field is performed to understand the effect of the Hartmann number proportional to the magnetic flux density. The inner cylinder rotates and the outer one is at rest, whereas the end walls, i.e., upper and lower walls, are stationary. The radius ratio, aspect ratio and Reynolds number are set to 0.5, 1.0 and 8000, respectively. Large-eddy simulation is conducted using the coherent structure model for the subgrid-scale stress tensor which realizes the laminarization by the Lorentz force. As increasing the Hartmann number, the small vortex structures are suppressed by the Lorentz force, and the orientations of the vortices change from the azimuthal direction to the axial direction. The vortices become the so-called quasi-two-dimensional (Q2D) vortices that align to the direction of the applied magnetic field. As for the streak structures of the azimuthal velocity in the vicinity of the inner wall, the high and low-speed streaky structures are advected with the flow velocity for low Hartmann numbers. For high Hartmann numbers, the low-speed streaky structures are suppressed and the high-speed streaky structures become triplet structures. Those structures move more slowly than the flow velocity in the vicinity of the inner wall.