[en] We study the quasi-bound state (QBS) spectra of the graphene quantum rings created by an axially symmetric electrostatic potential. Detailed calculations are carried out for the case of rectangular confinement potentials using the T-matrix and/or the local density of states approaches. Obtained results are analyzed in detail with respect to the two principal characters of QBSs, the (resonant) level position and the level width. A unique relation is established between the QBS-spectrum of a quantum ring under study and the resonant levels formed in the corresponding one-dimensional rectangular potential barrier. Studies are realized in both cases of zero and non-zero mass. (paper)