In order to improve the coupling efficiency of the semiconductor optical amplifier with a single mode fiber, a model of a tapered rib semiconductor optical amplifier is presented. The effects of the index of waveguide region, the width of tapered-rib end waveguide, the structure of rib waveguide and graded refractive index (GRIN) waveguide on the expanded output mode of the tapered rib waveguide are studied and calculated by using the finite element method. Coupling efficiency of 95% for the tapered-rib semiconductor optical amplifier and the single-mode fiber is obtained by optimizing the structure of the tapered rib semiconductor optical amplifier.