Far-infrared (FIR) interferometer is widely used to measure the electron density in the magnetically confined fusion plasma devices. A new FIR laser interferometer with a total of 13 channels (including 8 horizontal channels and 5 oblique channels) is under development for the HL-3 tokamak by using the formic-acid laser (HCOOH, f = 694 GHz). In order to investigate the boundary electron density activity, three horizontal interferometry channels located at Z = −97, −76, 76.5 cm have just been developed and put into operation in 2023 experimental campaign, with a time resolution of < 1.0 μs and line-integrated electron density resolution of ~ 7.0×1016 m−2. This paper mainly focuses on the optical design of the three-channel interferometry system, optical elements and recent experimental result on HL-3.