Investigations of beta-induced Alfvén eigenmodes (BAEs) destabilized by resonant magnetic perturbations (RMPs) have been conducted on the J-TEXT tokamak. In the Ohmic discharges, with RMPs having finite perturbed amplitudes, two different types of Alfvén eigenmodes have been observed and identified. One is considered as m-BAE, due to the strong correlation with magnetic island in some noticeable aspects, for example, frequency characteristic, mode number and driving mechanism. Specifically, the standing wave nodes of m-BAE are located at the O point and X point of the magnetic island. Another one is discerned as the magnetic island-induced AE (labeled as the MIAE-like mode in this work), which is consistent with the prediction of theory (Biancalani et al 2010 Phys. Rev. Lett. 105 095002). The frequency of MIAE-like mode is found to be approximately proportional to the square of magnetic island width.