Experimental and theoretical results are reported for photoionization of Ta-like (W+) tungsten ions. Absolute cross sections were measured in the energy range 16-245 eV employing the photon-ion merged-beam setup at the advanced light source in Berkeley. Detailed photon-energy scans at 100 meV bandwidth were performed in the 16-108 eV range. In addition, the cross section was scanned at 50 meV resolution in regions where fine resonance structures could be observed. Theoretical results were obtained from a Dirac-Coulomb R-matrix approach. Photoionization cross section calculations were performed for singly ionized atomic tungsten ions in their J = 1/2, ground level and the associated excited metastable levels with J = 3/2, 5/2, 7/2 and 9/2. Since the ion beams used in the experiments must be expected to contain long-lived excited states also from excited configurations, additional cross-section calculations were performed for the second-lowest term, J = 5/2, and for the 4F term, with J = 3/2, 5/2, 7/2 and 9/2. Given the complexity of the electronic structure of W+ the calculations reproduce the main features of the experimental cross section quite well.