We report on a continuous-wave (CW) and passively mode-locked operation of a fluorite-type Yb:BaF2 crystal. Pumped with a spatially single-mode, fiber-coupled InGaAs laser diode at 976 nm, the Yb:BaF2 laser generated a maximum CW output power of 512 mW at 1054.4 nm, corresponding to a laser threshold of 36.5 mW and a slope efficiency of 65.0%. A continuous wavelength tuning across 85 nm (1007-1092 nm) was achieved. By implementing a semiconductor saturable absorber mirror for initiating and sustaining the soliton pulse shaping, near Fourier-transform-limited pulses as short as 52 fs were generated at 1058.2 nm with an average output power of 129 mW at a pulse repetition rate of ∼79.5 MHz. To the best of our knowledge, this is the first report on the passively mode-locked operation of the Yb:BaF2 crystal.