- The nonlinear mean-field dynamo due to a shear-current effect in a nonhelical homogeneous turbulence with a mean velocity shear is discussed. The transport of magnetic helicity as a dynamical nonlinearity is taken into account. The shear-current effect is associated with the W × J term in the mean electromotive force, where W is the mean vorticity due to the large-scale shear motions and J is the mean electric current. This effect causes the generation of large-scale magnetic field in a turbulence with large hydrodynamic and magnetic Reynolds numbers. The dynamo action due to the shear-current effect depends on the spatial scaling of the correlation time τ(k) of the background turbulence, where k is the wave number. For Kolmogorov scaling, τ(k)∝k-2/3, the dynamo instability occurs, while when τ(k) ∝k-2 (small hydrodynamic and magnetic Reynolds numbers) there is no the dynamo action in a sheared nonhelical turbulence. The magnetic helicity flux strongly affects the magnetic field dynamics in the nonlinear stage of the dynamo action. Numerical solutions of the nonlinear mean-field dynamo equations which take into account the shear-current effect, show that if the magnetic helicity flux is not small, the saturated level of the mean magnetic field is of the order of the equipartition field determined by the turbulent kinetic energy. Turbulence with a large-scale velocity shear is a universal feature in astrophysics, and the obtained results can be important for elucidation of origin of the large-scale magnetic fields in astrophysical sheared turbulence.