Surgical teleoperation systems are being increasingly deployed. There are, however, remaining 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 offer a general approach to designing the overall control structure. This paper addresses these issues by proposing an optimized controller which guarantees robust stability and performance. The environment, i.e., soft tissues, is characterized with the nonlinear Hunt-Crossley model. The overall teleoperation system is modeled as a linear parameter-varying system. A gain-scheduling control scheme is adapted to design a performance-optimized controller while guaranteeing robust stability. The developed gain-scheduling control scheme shows good tracking capacity and high transparency in varied experimental conditions. Error of the transmitted impedance is significantly lower compared to other conventional control schemes for frequency band less than 2 Hz which is frequently recommended for surgical teleoperation.