This paper is devoted to the study of robust strict positive real stabilization of SISO uncertain systems, i.e. finding a single controller that not only robustly stabilizes a plant with uncertainties under unity-feedback but also makes the closed-loop system robustly strictly positive real. It is proved that there must exist a stable controller achieving robust strict positive real stabilization of uncertain systems with both parameter variations and unstructured uncertainties under some reasonable assumptions. The properness of the controller is guaranteed when the largest relative degree of an uncertain system is restricted. By applying these results to nonlinear systems, some significant conclusions on asymptotic hyperstability robustness are given.