Magneto-optical and time-resolved photoluminescence (PL) spectroscopies are employed to evaluate electronic structure of a bound exciton (BX) responsible for the 3.364 eV line (labeled as I * 1 ) in bulk ZnO. From timeresolved PL spectroscopy, I * 1 is concluded to originate from the exciton ground state. Based on performed magneto-PL studies, the g-factors of the involved electron and hole are determined as being g e = 1.98 and g h // ( g h ⊥ ) = 1.2 (1.62), respectively. These values are nearly identical to the reported g-factors for the I * line in ZnO (Phys. Rev. B 86, 235205 (2012)), which proves that I * 1 should have a similar origin as I * and should arise from an exciton bound to an isoelectronic center with a hole-attractive potential.