Numerical simulation of blood flows in patient-specific arteries is becoming an important tool in understanding vascular diseases and surgery planning. Depending on the branching geometry and the patient parameters, the flow can be quite complicated with local vortex structures and rotations, but the principal component of the flow is always along the centerline of the artery. Based on this observation, we introduce a new two-level domain decomposition method for unsteady incompressible Navier-Stokes equations in three-dimensional complex patient-specific arteries, and the key component of the preconditioner is a parameterized one-dimensional unsteady Navier-Stokes or Stokes coarse problem defined along the centerline of the artery. The one-dimensional preconditioner and some overlapping three-dimensional subdomain preconditioners are combined additively to form the two-level method via interpolations using radial basis functions. The most important feature of the method is that the cost of solving the coarse problem is nearly negligible compared with the subdomain solver. The blood flow is modeled by the unsteady incompressible Navier-Stokes equations with resistance outflow boundary conditions discretized by a stabilized finite element method on fully unstructured meshes and the second-order backward differentiation formula in time. Numerical experiments indicate that the proposed method is highly effective and robust for complex arteries with many branches, in other words, the number of linear and nonlinear iterations changes very little when the mesh is refined or the number of subdomains is increased or the number of arterial branches is increased.