Considering the significant influence of the asymmetric structure of the one-dimensional potential field on the stochastic resonance (SR), the research is extended to the two-dimensional asymmetric potential field. The Brownian particles moving in the Landau-type potential field served as the research object. According to the linear response theory and probability flow method, the analytical formula for the spectrum power amplification (SPA) of the physical system concerning the driving frequency is derived. When the SPA is used as a measurement index, the theoretical analysis shows that an atypical SR phenomenon occurs in the system. The reason is that as the noise intensity increases, the response mode changes due to the asymmetric structure of the Landau-type potential field. Moreover, the linear responses and the SPA are inversely proportional to the driving frequency. The conclusions of the theoretical analysis are verified by numerical simulation. Finally, the Landau-type potential system is applied to the bearing fault signal detection. The experimental results show that the Landau-type potential system can effectively diagnose the faults of the inner and outer ring of the bearings, which proves the application value of the Landau-type potential system.