Distributed optical fiber sensing based on Brillouin scattering is one of the subjects of intensive investigation all over the world at present. For the distributed fiber sensing based on Brillouin optical time-domain reflectometry, the heterodyne detection achieves the highest sensing resolution, and the key problem is how to obtain the referenced light with Brillouin frequency shift. The principle of frequency shift based on LiNbO3 waveguide electro-optic intensity modulator (EOIM) is analyzed in detail. The 11 GHz frequency shift at 1550 nm is obtained experimentally with a 15 Gbit/s LiNbO3 waveguide. It is convenient to change the optical intensity of the sidebands by tuning the DC bias voltage while the microwave modulation frequency and power are fixed. Particularly, when the DC bias voltage is set to 6.5 V, the modulator achieves minimum total output optical intensity, and the first sideband with Brillouin frequency shift reachs the maximums relative intensity and signal-to-noise ratio (SNR). These results can be used for Brillouin heterodyne detection in the distributed optical fiber sensing.