The localized coupling among geodesic acoustic mode (GAM), tearing modes (TMs) and twin counter-propagating beta-induced Alfvén eigenmodes (BAEs) waves has been investigated in the experimental advanced superconducting tokamak. Before the appearance of TMs, typical continuous GAM is observed through the multi-channel Doppler backscattering (DBS) diagnostic. The twin BAEs can be excited after the burst of magnetic islands, which are localized to the q = 4 rational surface that is confirmed by the measurement of DBS array, where the GAM and twin BAEs are observed synchronically at R ≈ 2.23 m (normalized radius ρ ≈ 0.8). One reasonable excitation mechanism is proposed that the twin BAEs can be excited by the nonlinear interaction between GAM and magnetic islands. As the width of magnetic islands increases, the electromagnetic twin BAEs increase synchronically with the decreasing of electrostatic GAM, strongly suggesting that the electromagnetic components are pumped from three-wave interaction between electrostatic GAM and magnetic islands.