In this paper a novel approach is proposed for interaction force estimation between a non-passive soft tissue in contact with end effector of a robot. It is necessary to understand the real behavior of living organs of the body in the robotic surgeries to do a better operation especially in cases of tele-operation surgery. In addition, this interaction force to the surgeon should be fed back in a successful surgery which is an important factor. In this paper, a model for a non-passive soft tissue is suggested. The model for the beating heart tissue that consists of a passive viscoelastic part as well as an active part that is considered as an unknown time-varying parameter. Afterward, the total interaction force between tissue and robot is estimated, using a similar approach to unknown input observers (UIO). The main difference between the proposed method and those in the literature is that unlike other UIO approaches, the proposed strategy does not use the derivative signal in estimating the active part of the interaction force. Finally, simulations and experiments are performed to demonstrate the effectiveness of the proposed force estimation approach.