The BaMgF₄ single crystal was grown by the temperature gradient technique. Highly pure MgF₂ and BaF₂powders were used as raw materials and CaF₂ single crystal was chosen as a seed to induce BaMgF₄ single crystal grow along 〈0 0 1〉 orientation. The short cut-off wavelength of BaMgF₄ single crystal was determined to be 130 nm which is consistent with the previously reported result. We realized second harmonic generation from 1064 nm to 532 nm laser, and 800 nm to 400 nm femtosecond laser in single domain BaMgF₄ by using birefringent phase matching. 355-nm-wavelength laser was produced by Sum-Frequency Generation from 1064-nm- and 532-nm-wavelength laser, which is the shortest coherent radiation obtained in the UV in the BaMgF₄ crystal.