This paper considers a design method of a discrete-time adaptive output feedback control system with a feedforward input based on almost strict positive realness (ASPR-ness). The proposed scheme utilizes the property of ASPR of the controlled plant, and the reference signal is used as feedforward input. The parallel feedforward compensator (PFC) which renders an ASPR augmented controlled plant is also investigated. Besides, it is shown that the output of original plant can track reference signal perfectly without any steady state error. The effectiveness of the proposed scheme is confirmed through a pilot-scale temperature control system.