Approximate/adaptive dynamic programming (ADP) has demonstrated great successes in the construction of datadriven output feedback optimal control for linear time-invariant systems and data-driven state feedback optimal control for nonlinear systems. This work investigates data-driven output feedback optimal control design for a class of nonlinear systems. It proposes to parameterize all admissible output feedback optimal control policies over accessible signals (system output and its time derivatives). In the case that system state can be parameterized as functions of accessible signals, then the value function and control policy can be parameterized over accessible signals, which allow ADP to be driven by accessible data. For a special case,where system state, value function and control policy can be linearly parameterized over a finite functional space over accessiblesignals, the policy iteration algorithm (PI) of ADP is reduced to solve a system of linear equations. Two data-driven PIs are developed to accomplish data-driven output feedback optimal control design. Simulation validates the proposed methodology.