Photoionization cross sections and dipole transition probabilities for the astrophysically important iron ion Fe IV are presented. The computations were carried out in the close coupling approximation using the R-matrix method including 31 LS terms with multiplicity and 5 of the target ion Fe V. All quartets and sextet bound states of Fe IV with and are considered. The results include 746 LS bound states, dipole oscillator strengths for 34 635 LS transitions, and, for all bound states, detailed photoionization cross sections with extensive resonance structures. These data differ significantly in many cases from the earlier data calculated under the Opacity Project and other theoretical calculations. In particular, the new cross section for the ground state of Fe IV exhibits a large resonance near the threshold that is not present in previous calculations and is likely to affect the effective photoionization rate significantly. The autoionizing state that corresponds to that resonance as well as the Rydberg series to which it belongs are identified through supplementary close coupling calculations.