Phase imaging without a phase wrapping ambiguity is required for wide-axial-range 3D imaging in the fields of surface topography measurement and biomedical imaging. Although multicascade-linked synthetic-wavelength digital holography (MCL-SW-DH) using an optical frequency synthesizer (OFS) is a promising method to meet this requirement, the slow switching of multiple optical wavelengths in the OFS prevents rapid imaging. In the work described in this article, a line-by-line spectral-shaped electro-optics-modulator-based optical frequency comb (EOM-OFC) is used as a light source in MCL-SW-DH to achieve rapid image acquisition. While MCL-SW-DH enables surface topography measurement with millimeter-order axial range and micrometer-order axial resolution, the line-by-line spectral-shaped EOM-OFC extracts a single narrow-linewidth OFC mode from the 10 GHz-spacing EOM-OFC at a center wavelength of 1545 nm within a spectral range of 30 nm at an interval of 500 ms. The effectiveness of the proposed MCL-SW-DH was highlighted by performing surface topography measurement with four step differences of sub-millimeter to millimeter size with an axial uncertainty of 2.08 µm in the image acquisition time of several seconds. The proposed MCL-SW-DH will be a powerful tool for 3D imaging with a wide axial range and high axial resolution.