The exact diagonalization is the most accurate approach for solving the Hubbard model. The approach calculates the ground state of the Hamiltonian derived exactly from the model. Since the Hamiltonian is a large sparse symmetric matrix, we usually utilize an iteration method. It has been reported that LOBPCG method with a shift-and-invert preconditioner using an approximate eigenvalue can solve the problem efficiently. However, the preconditioner does not take effect for the Hamiltonian whose off-diagonal elements are predominant. In this research, we apply the preconditioner using the Neumann expansion and propose the communication avoiding strategy in consideration of the physical property of the Hubbard model. We show that the preconditioner improves the convergence property and decreases the elapsed time for the Hamiltonian with the predominant off-diagonal elements.