The motion of gravitational axion-like particles (ALPs) around a Kerr black hole is analyzed, paying attention to the resonance and distribution of spectral radiation. We first discuss the computation of gR mu nu rho rho sigma R mu nu rho sigma and its implications with Pontryagin's theorem, and then a detailed analysis of Teukolsky's master equation is carried out. After carefully analyzing the Teukolsky master equation, we show that this system exhibits resonance when omega greater than or similar to mu, where mu is the mass of the ALP, while the homogeneous part of the solution exhibits the superradiance. A skew-normal distribution can approximate the energy distribution of the resonant modes, and we give explicit expressions for its lifetime.