Large Na0.5K0.5NbO3 (NKN) piezoelectric single crystals were obtained by seed-free solid-state crystal growth method, which is a traditional sintering grain growth process, with LiBiO3 used as a sintering aid. The largest dimension of the single crystals obtained was 11mmx9mmx3mm. In addition to the LiBiO3 doping content, temperature, and time effect of the crystal growth process was systematically investigated and considered from the kinetics point of view. With the assistance of Avrami analysis, parameters relevant to the crystal growth process were determined. Laue diffraction and transmission electron microscopy suggested an orthorhombic symmetry for the single crystalline structure. Dielectric-frequency-temperature measurements revealed an orthorhombic-tetragonal and tetragonal-cubic phase transition at 155 degrees C and 405 degrees C, respectively, both of which are typical of first-order transitions, and have a well-defined thermal hysteresis. Rayleigh analysis was performed regarding to the extrinsic reversible and nonreversible piezoelectric properties, and the result suggested a dominant intrinsic reversible piezoelectric contribution of 91.5% under E-0=1kV/cm AC amplitude. Such a single crystal growth process route is low cost and a relative simple preparation process.