We propose a graphene-based modulator integrated into currently used communication fibers. The graphene is directly built into the core of the fiber to ensure the coupling efficiency. The fiber is deliberately side-polished to enhance the light-graphene interaction. The two-dimensional model analysis method and three-dimensional finite difference time domain method are used to rigorously disclose the light modulation mechanism under the anisotropic graphene modeling, which is merely conducted in previous studies. Based on such a structure, a phase modulator with an arm length of 127 μm is numerically demonstrated with enhanced modulation efficiency. A quasi-linear relation between the phase change and chemical potential of graphene is found theoretically for the first time, providing a large linear dynamic range to control the phase of optical modulation.