Large-eddy simulation, which is a widely used method of computational fluid dynamics, can accurately simulate wall-bounded turbulent flows due to near-wall treatment. Through analyzing the similarities of the eddy viscosity formulations for large-eddy simulation and Reynolds-averaged Navier-Stokes, we propose a universal subgrid eddy viscosity model (USM) for large-eddy simulation of turbulent flows. The subgrid eddy viscosity in the model is related not only to the norm of the strain rate tensor of the smallest resolved scales but also to the mixing length associated with the subgrid scale, while the subgrid tensor is associated with the strain rate tensor of large scales like in the classical Smagorinsky model. With the friction-velocity-based Reynolds number, 395, the channel flow simulations by USM show that this subgrid eddy viscosity model can physically illustrate the eddy viscosity in the near-wall region and directly simulate the wall-bounded turbulent flow, compared with the classical Smagorinsky model, the dynamic Smagorinsky model, and Moser et al.'s direct numerical simulations (DNS).