Simulating blood flows in compliant arteries in 3D is a challenging multi-physics problem.The difficulties are due to the high nonlinearity of coupled equations.To overcome the difficulties,we study an inexact Newton-Krylov algorithm with a multilevel Schwarz preconditioner to solve the monolithically coupled fluid-structure system.We show that the proposed algorithm is scalable in terms of the iteration count and the total compute time on a supercomputer with a large number of processors.