Equivalent linear system method is the main method of nonlinear structural system random response analysis. While it would generate big error when the results of equivalent linear system method are used to analyze the structural dynamic reliability. Through minimum mean square error principle

general nonlinear system was converted to equivalent Duffing nonlinear system

based on which the structural dynamic reliability was analyzed. The accurate steady state analytic solution of Duffing nonlinear system can be worked out by FPK equation

so it is not only convenient but also accurate to analyze structural dynamic reliability by using the equivalent nonlinear system method. It is also shown that the analysis results of equivalent nonlinear system method presented here is reliable and the calculation accuracy is higher than equivalent linear system method apparently through the example analysis.