Electro-optic modulators are critical components of optical communication systems. With an increasing demand for the near-infrared spectrum in optical communication, the 2 μm mid-infrared band has emerged as a promising option for expanding the bandwidth of fiber optic communications. This study proposes a mid-infrared electro-optic modulator based on barium titanate on an insulator platform at a wavelength of 2 μm. Theoretical analyses and structural optimizations are performed on the barium titanate ridge waveguide and slow-wave electrode. The simulation results demonstrate that at a wavelength of 2 μm and a modulation length of 5 mm, the designed electro-optic modulator exhibits high modulation efficiency and achieves a large electro-optic bandwidth, with a half-wave voltage-length product (V_π·L) of 0.677 V·cm and a 3 dB electro-optic bandwidth of 229.6 GHz.