The purpose of this paper is to design a model-based bilateral teleoperation method to improve the feedback force and velocity/position tracking for robotic-assisted tasks (such as palpation, etc.) under constant and/or varying time delay with environment dynamic property. Time delay existing in bilateral teleoperation easily destabilizes the system. Proper control strategies are able to make the system stable, but at the cost of compromised performance. Model-based bilateral teleoperation is designed to achieve enhanced performance of this time-delayed system, but an accurate model is required. Design/methodology/approach Viscoelastic model has been used to describe the robot tool-soft tissue interaction behavior. Kevin-Boltzmann (K-B) model is selected to model the soft tissue behavior due to its good accuracy, transient and linearity properties among several viscoelastic models. In this work, the K-B model is designed at the master side to generate a virtual environment of remote robotic tool-soft tissue interaction. In order to obtain improved performance, a self perturbing recursive least square (SPRLS) algorithm is developed to on-line update the necessary parameters of the environment with varying dynamics. Findings With fast and optimal on-line estimation of primary parameters of the K-B model, the reflected force of the model-based bilateral teleoperation at the master side is improved as well as the position/velocity tracking performance. This model-based design in the bilateral teleoperation avoids the stability issue caused by time delay in the communication channel since the exchanged information become position/velocity and estimated parameters of the used model. Even facing with big and varying time delay, the system keeps stably and enhanced tracking performance. Besides, the fast convergence of the SPRLS algorithm helps to track the time-varying dynamic of the environment, which satisfies the surgical applications as the soft tissue properties usually are not static. Originality/value The originality of this work lies in that an enhanced perception of bilateral teleoperation structure under constant/varying time delay that benefits robotic assisted tele-palpation (time varying environment dynamic) tasks is developed. With SPRLS algorithm to on-line estimate the main parameters of environment, the feedback perception of system can be enhanced with stable velocity/position tracking. The superior velocity/position and force tracking performance of the developed method makes it possible for future robotic-assisted tasks with long-distance communication.