The mechanism of excitation of beta-induced Alfvén eigenmodes (BAEs) with magnetic islands larger than a threshold without energetic ions is studied. It is found that the nonlinear coupling between geodesic acoustic mode and magnetic islands can drive the pair of BAEs. The phase of BAEs to island should be π/2 to excite the BAEs and the magnetic island is larger than a threshold. The results are consistent with the experimental results shown in EAST(#86309). It implies that similar experimental results in other tokamaks, that BAEs excitation by magnetic islands without energetic ions, may be from the nonlinear coupling between islands and waves. It also implies that the existence of magnetic islands can make the excitation of BAEs easier in plasma with energetic ions, since the magnetic island can also increase the pressure gradient of energetic ions near the island separatrix. This predicts that BAEs may appear more frequently in the presence of magnetic islands in ITER.