Laser performances of a new Na+,Yb3+:CaF2 crystal under laser diode pumping were demonstrated. This crystal only operated in the self-Q-switched scheme, with laser wavelength of 1.05 μm, and minimum pump absorbed power of 30 mW corresponding to power density of 0.60 kW/cm2. On 5 W incident power, the repetition rate and width of the self-Q-switched pulses reached 28 kHz and 1.5 μs, respectively. By using a semiconductor saturable absorber mirror (SESAM), simultaneous transform-limited 1 ps passively mode-locked pulses, with the average output power of one laser beam 180 mW and the repetition rate of 183 MHz, were obtained under the self-Q-switched envelope induced by the laser medium. The corresponding pulse peak power arrived at 27 kW, indicating the promising application of Yb3+,Na+-codoped CaF2 crystals in achieving ultra-short pulses and high pulse peak power.