Superconducting infinite-layer (IL) nickelates offer a new platform for investigating the long-standing problem of high-temperature superconductivity. Many models were proposed to understand the superconducting mechanism of nickelates based on the calculated electronic structure, and the multiple Fermi surfaces and multiple orbitals involved create complications and controversial conclusions. Over the past five years, the lack of direct measurements of the electronic structure has hindered the understanding of nickelate superconductors. Here we fill this gap by directly resolving the electronic structures of the parent compound LaNiO2 and superconducting La0.8Ca0.2NiO2 using angle-resolved photoemission spectroscopy. We find that their Fermi surfaces consist of a quasi-2D hole pocket and a 3D electron pocket at the Brillouin zone corner, whose volumes change upon Ca doping. The Fermi surface topology and band dispersion of the hole pocket closely resemble those observed in hole-doped cuprates. However, the cuprate-like band exhibits significantly higher hole doping in superconducting La0.8Ca0.2NiO2 compared to superconducting cuprates, highlighting the disparities in the electronic states of the superconducting phase. Our observations highlight the novel aspects of the IL nickelates, and pave the way toward the microscopic understanding of the IL nickelate family and its superconductivity.