Electro-optic modulators are essential devices on silicon photonic chips in modern optical communication networks. This paper presents a compact, low-loss electro-optic modulator. The modulation efficiency is greatly improved by embedding the lower half of the slot waveguide into the buried oxide layer and inserting graphene at the junction. The interaction of graphene with an optical field in a waveguide is studied using the finite element method. The functions of phase modulation and absorption modulation are realized by changing the gate voltage to change the chemical potential of graphene. The semi-embedded slot waveguide optical modulator has a length of 50 µm. After simulation verification, it can be used as an electro-absorption modulator and can achieve a modulation depth of 26.38 dB and an insertion loss of 0.60 dB. When used as an electro-refractive modulator, it can be realized with a linear change of phase from zero to π; the total insertion loss is only 0.59 dB. The modulator has a modulation bandwidth of 79.6 GHz, and the energy consumption as electro-absorption and electro-refraction modulation are 0.51 and 1.92 pj/bit, respectively. Compared with common electro-optic modulators, the electro-optic modulator designed in this paper has a higher modulation effect and also takes into account the advantages of low insertion loss and low energy consumption. This research is helpful for the design of higher-performance optical communication network devices.