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The study and calculation of spectrum of networks can be used to describenetworks structure and quantify analysis of networks performance. The fractalM\"{o}bius octagonal networks, denoted by $Q_n$, is derived from the inverseidentification of the opposite lateral edges of fractal linear octagonalnetworks. In this paper, the normalized Laplacian spectrum of $Q_n$ isdetermined by two matrices $\mathcal {L}_A$ and $\mathcal {L}_S$. As animportant application of our results, some topological indices (multiplicativedegree-Kirchhoff index, the number of spanning trees) formulas of $Q_n$ areobtained.

The Normalized Laplacian Spectrum Analysis of Fractal Mobius Octagonal Networks and its Applications