For the cladding removed multimode fiber, when the refractive index of the external solution is close to the fiber core, it will cause refractive-index-matched coupling effect. In this work, the appearance of two index-matched points was observed. One of the index-matched point located at short wavelength, which had not been reported previously. Then, magnetic fluid was used as the external solution around the fiber core. As magnetic fields of different intensities were applied, the refractive-index-matched coupling effect occurred, which was different from that happening within isotropic solution. The observed phenomenon was mainly due to the anisotropy of the magnetic fluid under magnetic field. Based on the establishment of theoretical model and formulation of empirical equation, numerical simulations were also employed to further investigate the refractive-index-matched coupling within the anisotropic solution.