We consider a gauge-singlet complex scalar field Φ with a global U (1) symmetry that is spontaneously broken at some high energy scale f a . As a result, the angular part of the Φ-field becomes an axion-like particle (ALP). We show that if the Φ-field has a non-zero coupling κ to the Standard Model Higgs boson, there exists a large region in the (f a , κ) parameter space where the global U (1) symmetry-breaking induces a strongly first order phase transition, thereby producing stochastic gravitational waves that are potentially observable in current and future gravitational-wave detectors. In particular, we find that future gravitational-wave experiments such as LISA, BBO and aLIGO+ could probe a broad range of the energy scale 10 3 GeV f a 10 8 GeV, independent of the ALP mass. Since all the ALP couplings to the Standard Model particles are proportional to inverse powers of the energy scale f a (up to model-dependent O(1) coefficients), the gravitational-wave detection prospects are largely complementary to the current laboratory, astrophysical and cosmological probes of the ALP scenarios.