Hybrid event beds are the deposits from sediment gravity flows that change their rheological behavior through their passage, entraining muddy sediments and damping turbulence. Muddy facies of hybrid event beds are often associated with abundant mud clasts which show a wide variety of size and shape. The variation of clast occurrence in hybrid event beds is expected to preserve the information of entrainment and transport processes of muddy sediments in submarine density currents. However, previous analyses of hybrid event beds have focused on describing the overall clast occurrence rather than the statistical size and shape analyses because traditional shape parameters are incapable of characterizing the complex shape of mud clasts. Here, a new quantitative grain-shape analysis of mud clasts is conducted and allows visualization of the spatial variation of clast size and shape, which suggests the wide variety of origin and transport systems of entrained mud clasts. This new method revises the traditional elliptic Fourier analysis, substituting Fourier power spectra (FPS) for traditional elliptic Fourier descriptors to overcome the mirror-wise shape problem. Further, principal-component analysis is shown to capture significant shape attributes more effectively than traditional shape parameters. The proposed method is applied to mud clasts in sediment-gravity-flow deposits in the lower Pleistocene Otadai Formation, central Japan. Results imply that there are distinctive shape and size differences of mud clasts that are strongly associated with depositional facies rather than the distance from the source. The clasts have a higher angularity than other facies in the debrite intervals in hybrid event beds. It is also shown that clasts in sandy, structureless facies have different characteristics in shapes based on elongation and convexity compared to laminated facies. Comparison between different shape-analysis methods demonstrates that none of the traditional methods are able to visualize these trends as effectively as the method presented herein. These results highlight the importance of the quantitative shape analysis of sediment grains and the effectiveness of FPS-based elliptic Fourier analysis.