The transmission of orbital angular momentum (OAM) modes in grapefruit-type microstructure fiber(MOF)is studied. The fiber core is surrounded by grapefruit-type air holes with diameter of 3 μm. The refractive index difference between fiber core and air hole is large, so that the transmission light can be concentrated into the core and stable modes can be formed. Based on the finite element method, vector eigenmodes in the fiber are analyzed. The effective refractive indexes and the mode filed distributions of these modes are obtained. The results show that the transmission of ten OAM modes can be supported around the wavelength of 630 nm. The effective refractive index differences among OAM modes are larger than 0.01. The large effective refractive index difference can suppress mutual coupling among different modes, and improve the transmission performance of OAM modes in fiber. In addition, we use the special designed optical vortex Dammann gratings in experiments to detect the OAM1,1 and OAM-1,1 modes after transmitting for 1 m in MOF.