Abstract: Numerical methods based on unstructured meshes for the three-dimensional fluid-solid interaction problems have many applications in science and engineering. Most of the existing algorithms are based on the partitioned approach that the equations for the fluid and solid are solved separately using existing solvers by enabling them to share interface data with one another. The convergence of the partitioned approach is sometimes difficult to achieve because the method is basically a Gauss-Seidel type process and it may encounter the instability problem of the so-called added mass effect. Moreover, the parallel scalability of the solution algorithm is also an important issue when solving the large-scale problem. In contrast, the monolithic approach shows a more robust convergence and also eliminates the added mass effect even for complicated problems. In this work, a fully implicit and monolithic scalable parallel algorithm based on domain decomposition method is developed for the three-dimensional unsteady fluid-solid interaction problem. The governing equations are established based on the arbitrary Lagrangian-Eulerian framework, and a stabilized unstructured finite element method is employed for the discretization in space and a second-order fully implicit backward differentiation formula in time. An inexact Newton-Krylov method together with a restricted additive Schwarz preconditioner is constructed to solve the large, sparse system of nonlinear algebraic equations resulted from the discretization. The accuracy of the numerical method is verified by a benchmark problem of flows around an elastic obstacle. The numerical performance tests show that the fully implicit and monolithic method has good stability with large time step sizes and good robustness under different physical parameters, and a parallel efficiency of 91% was achieved for 3072 processor cores on the “Tianhe 2” supercomputer. The experimental results show that the proposed numerical method is expected to be applied for the numerical simulation of large-scale fluid-structure interaction problems in complex regions.