Yb^3  +  :  KY  (  WO₄₎₂ (Yb:KYW) possesses various excellent properties, such as its highly polarized emission cross section, that makes it an excellent option for developing highly efficient diode-pumped solid-state lasers. A high-energy, high-beam-quality passively Q-switched Yb:KYW laser was demonstrated. The small-signal gain characteristics of the Yb:KYW crystal under quasi-continuous-wave laser diode (LD) pumping were obtained by theoretical analysis. Under LD end-pumping at a repetition rate of 500 Hz and a pumping width of 200  μs, the Q-switched Yb  :  KYW  /  Cr^4  +  :  YAG laser operated at a wavelength of 1025 nm, and a single-pulse energy of 0.5 mJ was obtained with a pulse width of 5.8 ns. Near-diffraction-limited beam quality with an M² value of ∼1.02 was achieved. The compact setup provided efficient second-harmonic generation at 512.5 nm via type-I phase matching using a LiB₃O₅ (LBO) crystal, and the output single-pulse energy was 0.13 mJ. We believe that these results further demonstrate the utility of Yb:KYW as a passively Q-switched laser crystal for solid-state lasers, particularly for applications that require nonlinear frequency conversion.