Within a joint experimental and theoretical research project, double photoionization of the He-like B3+ ion by a single photon was studied in the energy range from approximately 350 to 1160 eV. With the parent-ion beam in the experiment containing both 1s21S ground-state (90.9%) and 1s2sS3 metastable B3+ ions (9.1%), two contributions to the apparent single- and double-ionization cross sections, σ34app and σ35app, respectively, are involved in the measurements. Ratios Y(5+)/Y(4+) of double- over single-ionization yields were experimentally determined. By multiplying the measured ratios by the known cross section σ34app, the apparent cross section σ35app for double ionization was inferred. Using the information thus obtained, the measured yield of B5+ ions produced from hydrogenlike B4+ could also be normalized. The results show good agreement with theoretical benchmark cross sections σ45 for single photoionization of B4+. Convergent close-coupling calculations were performed to determine double-photoionization cross sections σ35 for B3+(1s2) and B3+(1s2s) ions. The result for the ground state agrees very well with theoretical data obtained previously with an intermediate-energy R-matrix approach. Within the systematic uncertainty of the normalized experimental cross sections, calculated and measured data are in agreement with one another.