We report a molecular dynamics simulation of melting of tungsten (W) nanoparticles. The modified embedded atom method interatomic potentials are used to describe the interaction between tungsten atoms. The melting temperature of unsupported tungsten nanoparticles of different sizes are found to decrease as the size of the particles decreases. The melting temperature obtained in this study is approximately a decreasing function of inverse radius, in good agreement with the predictions of thermodynamic models. We also observed that the melting of a W nanoparticle is preceded by the premelting of its outer skin at a temperature lower than its melting temperature.