This paper is concerned with the perfectly matched layer (PML) for a lossy medium in terms of a finite volume time domain (FVTD) method based only on the Cartesian coordinate system. In this point-oriented FVTD method, there are no spatial differences between electric and magnetic fields. We can take account of the inhomogenity of the lossy medium by considering averaged material constants in each rectangular cell. Numerical examples are given for the electromagnetic wave propagation in two-dimensional tunnels with bends and branches.