In order to study the effective coupling between optical fiber and wide waveguide grating (≥30 microns), an expand core fiber is designed for a given wide waveguide grating of 30 microns based on the theory of coupling Gaussian beam into waveguide grating, by using the method of matrix optics technologies and Gaussian beam theories. After the coupling loss is analyzed, the model of coupling expand core fiber with waveguide grating is built. By optimizing the structure of the fiber, 10.8 microns waist radius of output beam is obtained theoretically. At last the structure tolerance of the expand core fiber is studied. And then the optical coupling efficiency imposed by the position of Gaussian beam on the grating is discussed by comparing the Gaussian beam output from expand core fiber, single mode fiber and free space Gaussian beam with waist radius of 16 microns. The results are that the position tolerance of the expand core fiber is more than that of single mode fiber and almost the same as that of Gaussian beam with waist radius of 16 microns.