Preconditioned iterative methods in an implicit unstructured grid solver of compressible flows are compared. The three-dimensional Euler and Navier-Stokes equations are discretized by the edge-based finite volume method. The artificial dissipation scheme for the inviscid numerical fluxes is developed for the unstructured grid from Jameson's scheme for the structured grid. The following methods are compared to the supersonic and transonic inviscid flows and subsonic viscous laminar and turbulent flows: the central difference methods with the scalar and matrix dissipation scheme and Roe's upwind method with the MUSCL scheme for the inviscid fluxes; the scalar and matrix dissipation method for the left-hand side operator in the implicit scheme; the ILU, DILU and SGS factorizations for the preconditioner; and GMRES and Bi-CGSTAB methods for the linear system solver. The results show that a combination of the matrix dissipation in the inviscid fluxes and the scalar dissipation in the left-hand side works better than the other *schemes. In the preconditioned iterative methods, a combination of DILU or SGS and the Bi-CGSTAB is recommended for the aspect of required memory.