In this paper, an adaptive model output following control utilizing almost strictly positive real (ASPR) characteristics of the plant is considered. The plant is said to be ASPR if there exists a static output feedback such that the resulting closed-loop transfer function is strictly positive real. A design scheme of an adaptive model output following control system having a simple structure is proposed for the ASPR plant. The ASPR condition imposes severe restrictions on the plant with relation to the practical application. However, we can construct an ASPR augmented plant, which is regarded as a virtually new controlled plant, by implementing a parallel feedforward compensator or pre-compensator on the plant. The design scheme of such compensators that make the non-ASPR plant virtually ASPR is proposed by taking plant uncertainties into consideration. As a result, the applicable class of the proposal can be expanded. The effectiveness of the proposed methods is confirmed through numerical simulations.