To investigate the surface structures of forsterite in crystalline and glassy states, we performed molecular dynamics calculations. The result shows that a low-density layer exists in the surface. The amplitude of the thermal vibrations of atoms in the surface layer is higher than that of the internal parts due to a low coordination number. The enhanced thermal vibrations of atoms in the surface layer cause a surface melting. The surface effects have important implications for forsterite states in meteorites and interstellar space.