We report a cold atom interferometer based on the lightest alkali metal ⁶Li and measure its recoil frequency precisely, measuring the fine-structure constant on a preliminary basis. To overcome the challenges associated with magnetic-field sensitivity caused by the half-integer spin of atoms, a magnetically insensitive Raman transition and a conjugated Ramsey-Bordé interferometer involving crossed Raman beams and coherence time >2.3 ms is realized. The error in the angles between Raman beams is eliminated using four sets of interferometers developed based on geometric relationships. The measured recoil frequency ω_r is2π×73 672.789(36) Hz, and the fine-structure constant is 1/137.035976(33). These values indicate the most accurate measurements for ⁶Li obtained using the reported atom interferometer. The implementation of the ⁶Li cold atom interferometer not only enriches the elements of atom interferometers, but also has great potential in the field of precision measurement due to its high recoil frequency.