The finite difference time domain (FDTD) computational zone was truncated by an artificial boundary, of which the geometric shape was conformal with the boundary of an arbitrary shaped scatterer. The external conformal mesh was generated by the Thompson transformation.On the truncating boundary, the time domain measured equations of invariance (MEI) were applied as a local absorbing boundary condition. So the FDTD computational domain was compressed remarkably. The numerical experiment proved that the requirement of computer storage is reduced while the numerical accuracy is not decreased.