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The oil‐paper compound insulation plays a vital role in the insulation structure of power transformer. To obtain the characteristics of the transformer's insulation system, it is of great importance to study the dielectric response of oil‐paper compound insulation. In this study, fractional calculus is applied to model the oil‐paper compound insulation. Both low‐frequency and broadband high‐frequency models are proposed and then they are verified by fitting the measured data of different insulation papers. Finally they are applied to two different cases: (i) the low‐frequency model for fitting polarity reversal property; (ii) the broadband high‐frequency model for studying the influence of the parameters variations on the frequency domain spectroscopy (FDS). The results demonstrate the advantages of the proposed models when compared with traditional ones. [ABSTRACT FROM AUTHOR]