Abstract Dynamics of magnetization M driven by microwave are derived analytically from the nonlinear Landau-Lifshitz-Gilbert equation. Analytical M and susceptibility are obtained self-consistently under a positive circularly polarized microwave field, h=(hcosωt,hsinωt,0), with frequency ω, which is perpendicular to a static field, H=(0,0,H). It is found that the orbital of M is always a cone along H. However, with increasing h the polar angle θ of M initially increases, then keeps 90° when h≥h 0=αω/γ in ferromagnetic resonance (FMR) mode, where α is Gilbert damping constant and γ is gyromagnetic ratio. These effects result in a nonlinear variation of FMR signal as h increases to h≥h 0, where the maximum of resonance peak decreases from a steady value, linewidth increases from a decreasing trend. These analytical solutions provide a complete picture of the dynamics of M with different h and H.