Tuning the electronic properties of low-dimensional materials is helpful in building nano electronic devices. Here, we investigate the structural and electronic structures of one-dimensional helical Se atomic chain by using first-principles calculations. Our results show that this structure has a much lower energy than the one with a straight-line structure. Our phonon calculations and ab initio molecular dynamics simulations suggest that this structure is both dynamically and thermally stable. The band structure shows that it is a semiconductor with a gap of about 2.0 eV and Rashba-type splitting near the X point. The helical structure is good for tuning the electronic properties by using strains. As a result, a 5% strain leads to a 20% change in the band gap while the Rashba energy offset is doubled. Moreover, we find that the valence band is a flat band, over which hole doping can induce ferromagnetism and the system becomes half-metallic. Further increasing the doping level can transform the system into a ferromagnetic metal. Such a strategy is then applied to one-dimensional helical Te atomic chain and similar results are obtained.