We investigated the effects of single electron charging energy in high temperature superconductors. Various phenomena originating from Coulomb blockade were observable in superconducting tunnel junctions. High quality tunneling junctions were fabricated from c-axis oriented NdBa2Cu3O7–delta/PrBa2Cu3O7–delta/NdBa2Cu3O7–delta thin film multilayers by the pulsed laser deposition method. The current-voltage characteristics (CVCs) show a Coulomb gap for Cooper pair tunneling when the charging energy exceeds the Josephson coupling energy. We found a regime in which the CVCs exhibit sharply defined Coulomb steps due to single electron dynamics and nonlinear tunneling rates. From the obtained Coulomb staircase, the tunneling resistance shows a quantum effect: It is modulated by the tunneling current in the form h/4e2RT~[sin(piI/I0)2/(piI/I0)]. We suggest an interpretation involving the quantum resistance h/e2 and the competition between the charging, Josephson, and thermal energies of the system. Our results give a perspective on a solid-state quantum system with considerable interest for direct application in quantum computing.