Accurate numerical simulation of fluid flows around wind turbine plays an important role in understanding the performance and also the design of the wind turbine. The computation is challenging because of the large size of the blades, the large computational mesh, the moving geometry, and the high Reynolds number. In this paper, we develop a highly parallel numerical algorithm for the simulation of fluid flows passing three-dimensional full size wind turbine including the rotor, nacelle, and tower with realistic geometry and Reynolds number. The flow in the moving domain is modeled by unsteady incompressible Navier-Stokes equations in the arbitrary Lagrangian-Eulerian form and a non-overlapping sliding-interface method is used to handle the relative motion of the rotor and the tower. A stabilized moving mesh finite element method is introduced to discretize the problem in space, and a fully implicit scheme is used to discretize the temporal variable. A parallel Newton-Krylov method with a new domain decomposition type preconditioner, which combines a non-overlapping method across the rotating interface and an overlapping Schwarz method in the remaining subdomains, is applied to solve the fully coupled nonlinear algebraic system at each time step. To understand the efficiency of the algorithm, we test the algorithm on a supercomputer for the simulation of a realistic 5MW wind turbine. The numerical results show that the newly developed algorithm is scalable with over 8000 processor cores for problems with tens of millions of unknowns.