Abstract: Pump coupler is the key passive optical device of the high-power fiber laser. Its producing process is the side-fusing of the pump fiber and the main fiber. This producing process can keep the insertion loss of the main fiber low, but the angle between the pump fiber and the main fiber has a great influence on the coupling efficiency. In order to solve this problem, the theoretical model was established according to the structural characteristics of the fused sidepump coupler. The equations of the power and the fiber angle were derived. The simulation results were obtained and were demonstrated by the experiments. The conclusions are as follows: the pump coupling efficiency gradually increases with the decrease of the fiber angle between the pump fiber and the main fiber, but the critical fiber angle exists. When the numerical aperture (NA) of the pump fiber is smaller, the couple efficiency and the critical angle are larger. The critical fiber angle is 9.7 and the maximum coupling efficiency is 96.9% when the pump fiber NA is 0.22. The critical fiber angle is 11.5 and the maximum coupling efficiency is 97.8% when the pump fiber NA is 0.15. The conclusions are instructive for the designs and the productions of the highpower fiber coupler.