The nonlinear scattering loss in the single-mode fiber is analyzed. It is proved theoretically and experimentally that the maximal transmitting power in an optical fiber is limited by the stimulated Brillouin scattering (SBS). Based on mode field coupling theory, a model to calculate the butt-joint coupling efficiency between a multi-mode fiber and a single-mode fiber is presented. The dependence of the coupling efficiency between the multi- and single-mode fibers on the core radius of the multi-mode fiber is investigated. A experiment is conducted with 532 nm laser, multi-mode fiber (NA=0.11, a=12.5 μm) and single-mode fiber (NA=0.11, a=1.75 μm) to measure the butt joint coupling efficiency of multi-mode fiber to single-mode fiber. Good agreement is obtained between the experimental results and the theoretical predictions. A combined multi- and single-mode fiber relay system is proposed to transport laser beams with high power and good beam quality.