Abstract Observations of stars in the the solar vicinity show a clear tendency of old stars to have larger velocity dispersions. This relation is called the age–velocity dispersion relation (AVR) and it is believed to provide insight into the heating history of the Milky Way galaxy. Here, in order to investigate the origin of the AVR, we performed smoothed particle hydrodynamic simulations of the self-gravitating multiphase gas disks in the static disk-halo potentials. Star formation from cold and dense gas is taken into account, and we analyze the evolution of these star particles. We find that exponents of simulated AVR and the ratio of the radial to vertical velocity dispersion are close to the observed values. We also find that the simulated AVR is not a simple consequence of dynamical heating. The evolution tracks of stars with different epochs evolve gradually in the age–velocity dispersion plane as a result of: (1) the decrease in velocity dispersion in star-forming regions, and (2) the decrease in the number of cold/dense/gas as scattering sources. These results suggest that the AVR involves not only the heating history of a stellar disk, but also the historical evolution of the ISM in a galaxy.