As a part of a project devoted to the study of the Ursa Minor dwarf spheroidal (dSph) galaxy, the star formation history of the galaxy is presented. The analysis uses wide-field photometry, encompassing about 1°×1° (the total covered area being 0.75 deg2), which samples the galaxy out to its tidal radius. Derivation of the star formation history (SFH) has been performed using the synthetic partial-model technique. The resulting SFH shows that Ursa Minor hosts a predominantly old stellar population, with virtually all the stars having formed earlier than 10 Gyr ago and 90% having formed more than 13 Gyr ago. Nevertheless, the Ursa Minor color-magnitude diagram shows several stars above the main, old turnoff forming a blue plume (BP). If these stars were genuine main-sequence stars, Ursa Minor would have maintained a low star formation rate extending up to ~2 Gyr ago. However, several indications (relative amount and spatial distribution of BP stars and difficulty of retaining processed gas) argue against this possibility. In such a context, the most reliable hypothesis is that BP stars are blue stragglers originating in the old population, with Ursa Minor hence remaining the only Milky Way dSph satellite to host a pure old stellar population. A marginally significant age gradient is detected, in the sense that stars in outer regions are slightly younger on average. The distance of Ursa Minor has been calculated using the magnitude of the horizontal branch and a calibration based on Hipparcos data for main-sequence subdwarfs. We estimate a distance of 76+/-4 kpc, which is slightly higher than previous estimates. From the red giant branch color, we estimate a metallicity [Fe/H]=-1.9+/-0.2, in agreement with a previous spectroscopic determination. No metallicity gradients have been detected across the galaxy.