Surgical teleoperation systems are being increasingly deployed recently. There are, however, some unsolved issues such as nonlinear characteristics of the interaction between the slave robot and soft tissues and difficulty in employing force sensors in the surgical end-effectors of the slave. These issues make it difficult to generalize any approach to develop a control for the system. This paper addresses these issues by proposing a H-infinity suboptimal controller preserving robust stability and performance. The environment, i.e., soft tissues, is characterized with the nonlinear Hunt-Crossley model. This nonlinear characteristics of soft tissues are expressed with an affine combination of linear models within a predefined parameter polytope. For this linear parameter-varying system, a gain-scheduling control scheme is employed to design a suboptimal controller while guaranteeing its stability. To avoid using any force measurement in slave, we used position-position (PP) control architecture. The developed gain-scheduling control is validated with quantitative experimental results. The developed gain-scheduling PP control scheme shows good tracking capacity and high transparency for varied experimental conditions. Error of the transmitted impedance is significantly lower compared with other conventional control schemes for frequencies less than 2 Hz, which is frequently recommended for surgical teleoperation.