Determining a good initial structure in the inverse design of electromagnetic devices based on topology optimization method is an important problem that has been relatively little studied. In this letter, a method for constructing the initial structure of a multi-frequency nanophotonic device by combining time reversal theory and principal component analysis is proposed, and the inverse design of two-dimensional 1×2 and 1×3 wavelength demultiplexers is taken as examples. The results show that the iterative optimization converges to a better figure of merit after using the proposed method, compared to classical and single-frequency initial structures. The proposed method also shows good adaptability when the design target changes.