Lattice Boltzmann method is a popular approach in computational fluid dynamics, and it can be used explicitly or implicitly. The explicit methods require small time step size which is not desirable. In the fully implicit case, existing approaches either lack a scalable and robust parallel nonlinear solver, or don’t allow the mesh to be fully unstructured preventing the method to be used for the simulation of fluid flows in large domains with complex geometry. In this paper, a parallel fully implicit second-order finite volume lattice Boltzmann method for incompressible flows on unstructured grids is introduced. The lattice Boltzmann equation is discretized by a finite volume method in space and an implicit backward Euler scheme in time. The resulting large sparse nonlinear system of algebraic equations is solved by a highly parallel Schwarz type domain decomposition preconditioned Newton-Krylov algorithm. The proposed method is validated by three benchmark problems with a wide range of Reynolds number: (a) pressure driven Poiseuille flow, (b) lid-driven cavity flows, and (c) viscous flows passing a circular cylinder. The numerical results show that the proposed method is robust for all the test cases and a superlinear speedup is obtained for solving a problem with over ten million degree of freedoms using thousands of processor cores.