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It was difficult to diagnose the complex analog circuit on line on the situation which some elements failed because of its various tolerance error and multiplex coupling relationship. Firstly, the quantitative mathematics process of diagnosing the complex analog circuit was given in this paper, and the method of picking voltage-frequency characteristic value was proposed, too. Secondly, the coupling method of principal component analysis and linear discriminant analysis was applied, thus the attribute covariance matrix, the between class scatter matrix and the within class scatter matrix were found. In this way the failure sample dimensions of the complex analog circuit were depressed. Finally, the failure data were precisely matched with the failure modes by applying the back propagation neural network. It was proved by the experiment result that the method of this paper was effective in the domain of depressing samples, classifying data and diagnosing failure. The accurate rate of classifying failure is a hundred percent,and the data sample dimension was reduced from 31 to 3. Compared with other four methods, such as discriminant analysis, principal component analysis and kernelized principal component analysis, the method of this paper was superior to these in respect of classifying data, depressing samples, etc.