Continuous-wave single-frequency tunable 544- and 272-nm beams have been demonstrated by the second- and fourth-harmonic conversions of a 1088-nm fundamental beam from a diode-oscillator fiber-amplifier. The single-pass second-harmonic generation with a MgO-doped periodically poled stoichiometric LiTaO3 crystal and the external-cavity frequency-doubling technique with a bulk BBO crystal were employed to achieve an approximately 6-W 544-nm beam and a 1.5-W 272-nm beam, respectively. We characterized the second- and fourth-harmonic generations and discussed their applications to calcium spectroscopy.