Once there is a global U(1) symmetry broken at a high-energy scale f_a, we will have a light axion-like particle (ALP) from the spontaneous symmetry breaking. In a large parameter space, the global U(1) symmetry breaking induces a strongly first order phase transition, thereby producing stochastic gravitational waves (GWs). A broad range of the U(1) breaking scale f_a can be probed in the GW experiments, i.e. from 10^3 GeV to 10^8 GeV. All the ALP couplings to the Standard Model particles are proportional to inverse powers of the energy scale f_a, and the GW prospects are largely complementary to the current low-energy laboratory, astrophysical and cosmological probes of ALPs.