Unconventional Cooper pairing originating from spin or orbital fluctuations has been proposed for iron-based superconductors. Such pairing may be enhanced by quasi-nesting of two-dimensional electron and hole-like Fermi surfaces (FS), which is considered an important ingredient for superconductivity at high critical temperatures (high-T-c). However, the dimensionality of the FS varies for hole and electron-doped systems, so the precise importance of this feature for high-T-c materials remains unclear. Here we demonstrate a phase of electron-doped CaFe2As2 (La and P co-doped CaFe2As2) with T-c = 45 K, which is the highest T-c found for the AEFe(2)As(2) bulk superconductors (122-type; AE = Alkaline Earth), possesses only cylindrical hole-and electron-like FSs. This result indicates that FS topology consisting only of two-dimensional sheets is characteristic of both hole-and electron-doped 122-type high-T-c superconductors.