Abstract: The flow around a cylinder is a typical flow pattern in the liquid metal blanket in Tokomak fusion device, which reveals significant influence on the relevant flow and heat transfer. In the present work, three-dimensional direct numerical simulations (DNSs) are performed to study the turbulent flows past a circular cylinder at Re=3900 under magnetic fields. For the case without magnetic fields, the DNS results are in good agreement with the available experimental and numerical results. With the increase of the flow distance in the downstream wake of the cylinder, the mean streamwise velocity profile varies from U-shaped to V-shaped and flattens out, indicating that the influence of cylinder on the flow structures weakens gradually. Within the shear layers, because of the Kelvin-Helmholtz instability, the shedding of the small-scale shear vortices can be observed clearly through the flow visualization. Taking the results of non-magnetic field as the initial condition, the magnetic fields along the streamwise direction are applied, where the corresponding Hartmann numbers (Ha) are 20, 40 and 80. When the magnetic field is weak, the three-dimensional turbulent properties are still clear, although the magnetic field inhibits the velocity field. As the magnetic field increases, the recirculation zone behind the cylinder is elongated. The shear layers near the cylinder become smoother and the corresponding destabilizing position shift downstream. Since the vortices in the wake are squeezed by Lorentz force in the vertical direction, the Karman vortex street gradually gets narrow with the increase of magnetic field. Meanwhile, the scale of the vortex structures becomes smaller compared with those without magnetic fields because of the dissipation effect of magnetic fields. This research not only extends the parameter range of turbulence under magnetic fields, but also shows important theoretical guiding value and engineering application value for the design and safe operation of the blanket.