We demonstrate a high power continuous-wave (CW) and acoustic-optically (AO) Q-switched 1314-nm laser with a diode-side-pumped Nd:YLF module. A maximum CW output power of 21.6 W is obtained with a diode pump power of 180 W, corresponding to an optical-to-optical conversion efficiency of 12.0% and a slope efficiency of 16.1%. In the Q-switching operation, a highest pulse energy of 3.8 mJ is obtained at a pulse repetition rate of 1 kHz. The shortest pulse width and maximum single peak power are 101.9 ns and 37.3 kW, respectively.