CT slice data and data files from CT scans of four fossil specimens of Charnia masoni from the Verkhovka Formation of Russia, alongside the publication arising from this work (Dunn et al., 2021) and associated photographs of the specimens. Specimens SOLZ 1, SOLZ 2, SOLZ 3 and SOLZ 6 were scanned and photographed at the University of Bristol, having been discovered during fieldwork on the White Sea coast in July 2017 (see the associated field photographs folder). Each specimen is a partial specimen of a 3D-preserved Charnia masoni. For each specimen, individual folders contain the tif stack of slice images; vg-project files related to VG Studio Max; and RAW and xtekct files for data reconstruction. These specimens represent important material of Charnia masoni, and are unusual in being three-dimensionally preserved. They are therefore perfect for non-destructive CT scanning to reveal their 3D morphology, as part of a collaboration with IPGG Novosibirsk. Specimens will reside permanently in the museum collections of IPGG Novosibirsk. For more information, please see; DOI: 10.1126/sciadv.abe0291