In this paper, a novel adaptive dynamic programming (ADP) algorithm, named output-feedback hybrid iteration (HI),is proposed to address the adaptive optimal control problem of discrete-time linear systems. The proposed output-feedback HI strategy learns the optimal control policy through two phases. First, a novel data-driven value-iteration (VI) scheme is employed to learn an admissible output-feedback control policy using the input/output data without relying on the knowledge of system matrices. Then, with the obtained admissible control policy, the optimal output feedback-control policy is approximated with an accelerated convergence rate through output-feedback policy iteration (PI). Online input/output data are utilized to reconstruct the full state of the system and integrated into the new output-feedback HI algorithm. Simulation results are presented and demonstrate the efficacy and practicality of the proposed output-feedback HI approach in comparison with traditional PI and VI techniques.