The purpose of this letter is to introduce an absorbing boundary condition for use with TLM simulations of open region field problems. The method is based on the wave impedance of a plane wave crossing an observation plane at an arbitrary angle, and is coupled to an algorithm to predict this angle. The impedance applied to the mesh boundary varies with the changing field distribution and is therefore referred to as a variable impedance boundary condition. Initial results indicate the proposed condition is an accurate method of modelling free space boundaries.