We propose a scenario in which a strong Peccei-Quinn (PQ) symmetry breaking in the early universe results in large inhomogeneities of the initial QCD axion field value, leading to the formation of very dense axion bubbles. Some of the axion bubbles subsequently collapse into primordial black holes (PBHs). The spatially homogeneous part of the QCD axion explains dark matter of the universe, while the PBHs arising from the axion bubbles can explain the LIGO events or the seed of supermassive black holes. Interestingly, the mass of PBH is determined by the axion decay constant; for fa = 1017 (1016) GeV, the PBH mass is heavier than about 10 (104) Mo˙. In addition, axion miniclusters are also formed from the axion bubbles more abundantly than PBHs, and their masses are expected to be heavier than in the usual scenario based on the spontaneous breaking of the PQ symmetry after inflation.