A molecular dynamics simulation based on the embedded-atom method was conducted at different sizes of single-crystal Ag nanoparticles (NPs) with diameters of 4 to 20 nm to find complete melting and surface premelting points. Unlike the previous theoretical models, our model can predict both complete melting and surface premelting points for a wider size range of NPs. Programmed heating at an equal rate was applied to all sizes of NPs. Melting kinetics showed three different trends that are, respectively, associated with NPs in the size ranges of 4 to 7 rim, 8 to 10 nm, and 12 to 20 nm. NPs in the first range melted at a single temperature without passing through a surface premelting stage. Melting of the second range started by forming a quasi-liquid layer that expanded to the core, followed by the formation of a liquid layer of 1.8 nm thickness that also subsequently expanded to the core with increasing temperature and completed the melting process. For particles in the third range, the 1.8 nm liquid layer was formed once the thickness of the quasi-liquid layer reached S rim. The liquid layer expanded to the core and formed thicker stable liquid layers as the temperature increased toward the complete melting point. The ratio of the quasi-liquid layer thickness to the NP radius showed a linear relationship with temperature.