The asymmetric system has stronger signal amplification ability. A new two-dimensional asymmetric bi-stable stochastic resonance (NTABSR) system is proposed. First, the theoretical analysis of the output signal-to-noise ratio (SNR) is implemented under the adiabatic approximation theory. The influence of each system parameter on the SNR of the system is analyzed. Experimental results show that the system can obtain higher output SNR by changing the asymmetry factor while other parameters remain fixed. Then, the system is applied to diagnose fault signals of two different bearings. The system parameters are optimized through the adaptive genetic algorithm, and the detection results are obtained. The final results show that the performance of the NTABSR system is better than that of the TSBSR system. This provides good theoretical support and application value for subsequent theoretical analysis and practical engineering.