We present the star formation history (SFH) and its variations with galactocentric distance for the Local Group dwarf galaxy of Phoenix. Color-magnitude diagram was obtained from WFPC2@HST reaching the oldest main sequence turnoffs. The IAC-star and IAC-pop codes and the MinnIAC suite have been used to obtain the star formation rate as a function of time, metallicity, and radius. We find that Phoenix has had ongoing but gradually decreasing star formation over nearly a Hubble time. The highest level of star formation occurred from the formation of the galaxy till 10.5 Gyr ago, when 50% of the total star formation had already taken place. From that moment, star formation continues at a significant level until 6 Gyr ago, and at a very low level till the present time. The chemical enrichment law shows a trend of slowly increasing metallicity as a function of time till 8--6 Gyr ago, when Z starts to increase steeply to the current value. Young stars are found in the inner region of the galaxy only, but intermediate-age and old stars can be found at all galactocentric distances. This study shows that star formation started at all galactocentric distances in Phoenix at an early epoch. Our results are compatible with a scenario in which the star formation region envelope slowly shrinks as time goes on, possibly as a natural result of pressure support reduction as gas supply diminishes. As a consequence, star formation stopped first in outer regions and the scale-length of the stellar mass density distribution decreased with time. No traces of a true, old halo are apparent in Phoenix either in its stellar age distribution or in the stellar mass density distribution, at least out to 0.5 kpc (about 2.5 scale-lengths) from the center.