Theoretical calculations based on the density functional theory and the Boltzmann semi-classical transport theory have been carried out to examine the structural, elastic, electronic, optical and thermoelectric properties of Potassium- and Yttrium-based half-Heusler (HH) compounds KYX (X = Ge, Sn and Pb). Based on our calculations, KYGe, KYSn, and KYPb HH compounds are mechanically stable, and show semiconductor nature with direct band gaps of 0.852, 0.921, and 0.927 eV, respectively, which are obtained from mBJ level of theory. Moreover, the KYSn is brittle, while the KYGe and KYPb are dutile. The optical results show that these HH compounds have wide absorption band from high energy region of infrarred to ultraviolet region. At high photon energies (beyond of 13 eV), they shows very small reflectivity. Because of their favorable electronic structure, these materials have very good thermoelectric performance with high thermopower and figure of merit. The effect of temperature on thermoelectric properties also is discussed in details.