The star formation history (SFH) of the Pegasus dIr, a likely Local Group member at 0.95 Mpc from the Milky Way, is investigated. We characterize the SFH by two basic functions: the star formation rate, psi (t), and the chemical enrichment law, Z(t). It has been derived by comparing the color-magnitude diagram of the resolved stars in Pegasus, with a total of 189 model diagrams produced with different psi (t) and Z(t) laws. The models in better agreement with the data indicate that star formation began in Pegasus about 15 Gyr ago and was larger, on average, during the first half than during the second half of the galaxy's life. During the most recent epoch, for which the SFH can be obtained with much better time resolution, the star formation seems to be produced in a bursting mode. This may have been the case for the whole life of the galaxy, although the resolution in time towards older epochs is not good enough to actually detect it. As for the chemical enrichment law, the best way to account for the observed metallicity of the galaxy (Z_f=0.002(+0.002}_{-0.001) ) is that it suffered a prompt initial chemical enrichment. This would be the case if infall was important, at least during the primeval epoch of galaxy evolution and points to a picture in which the galaxy began forming stars and enriching its interstellar medium in an early phase of collaps, when a lot of gas had still to be added to it. Pegasus and NGC 6822 are the only dIrs for which the kind of analysis presented here has been done. The fact that, like Pegasus, NGC 6822 also shows an important old to intermediate-age stellar population indicates that the Baade's sheet observed in most dIr, may in fact be the signature of an important population of old stars and suggest that dIr actually are old objects populated by large numbers of old stars. The mass in stars and stellar remnants is derived from average of the best model SFHs obtained. The percentage of dark matter in Pegasus that cannot be accounted for with stellar remnants or with an extrapolation of the Kroupa et al. IMF down to ~ 0.1 M_sun turns out to be ~ 92%.