A new efficient multiple-scattering theory is proposed to study XAFS spectra, which is based on partitioning method developed by one of the authors. This method includes important multiple-scatterings in infinite order, which is similar to the finite path-by-path approach. We also obtain some symmetric relations and recurrence formulas of free electron propagators G L L ′ to save the storage memory. Some illustrative examples are shown. For small systems the partial sum convergence is easily attained, however the efficiency is not so remarkable compared with the corresponding full multiple scattering calculation. The partial sum convergence is rather slow for large closely packed systems such as iron crystals, however it is accelerated by use of damping effects of photoelectron waves; the computation time is only about 5% of that by the full multiple scattering calculation for a cluster with 27 Fe atoms. However the damping effects play a minor role for loosely packed system such as Si crystals.