Bearing is very important for rotating machinery, whose faults even cause the fatal accident. However, the fault-induced impulses, which are in the vibration data, are too weak to be detected. To enhance the weak impulses and detect the bearing fault, a novel adaptive underdamped stochastic resonance (AUSR) based on neural network (NN) and cuckoo search algorithm (CS) called NNCS-AUSR is proposed. In the proposed method, local signalto-noise ratio (LSNR) is used to evaluate the AUSR output, NN to predict the range of the integral step that is one of AUSR parameters, and CS to search the optimal AUSR parameters. To verify the proposed method, bearing fault signals under different fault types, different fault levels and different motor loads are analyzed. Adaptive overdamped stochastic resonance based on CS (CS-AOSR) and AUSR based on CS (CS-AUSR) and are also used for comparison. The results show that NNCS-AUSR enhances the weak fault-induced impulses under various conditions more effectively and takes less time than CS-AOSR and CS-AUSR.