The mechanism based on graded-index fiber (GIF) is provided for efficient coupling between laser diode (LD) and single mode fiber (SMF). As the central component, the GIF is placed in front of SMF. A large-sized elliptical core is designed in GIF for matching the far field of LD, and the beam from LD can be focused and coupled into SMF. By analyzing with finite difference beam propagation method, the power coupling efficiency is able to reach 88%. For 1 dB insert loss, the tolerance in fiber length of GIF is 75 μm, and the tolerances of offset in the direction of major axis and minor axis are 28 μm and 10 μm, respectively. The scheme is useful for the design of high power LD coupling single mode tail fiber.