We present a comprehensive study of the low-energy band structure and Fermi surface (FS) topology of ACo2As2 (A = Ca, Sr, Ba, Eu) using high-resolution angle-resolved photoemission spectroscopy. The experimental FS topology and band dispersion data are compared with theoretical full-potential linearized augmented-plane-wave (FP-LAPW) calculations, which yielded reasonably good agreement. We demonstrate that the FS maps of ACo2As2 are significantly different from those of the parent compounds of Fe-based high-temperature superconductors. Further, the FSs of CaCo2As2 do not show significant changes across its antiferromagnetic transition temperature. The band dispersions extracted in different momentum (kx , ky ) directions show a small electron pocket at the center and a large electron pocket at the corner of the Brillouin zone (BZ). The absence of the hole FS in these compounds does not allow nesting between pockets at the Fermi energy (EF), which is in contrast to AFe2As2-type parent compounds of the iron-based superconductors. Interestingly, we find that the hole bands are moved 300-400 meV below EF depending on the A element. Moreover, the existence of nearly flat bands in the vicinity of EF are consistent with the large density of states at EF. These results are important to understand the physical properties as well as the possibility of the emergence of superconductivity in related materials.