Wires and pulleys drive instruments attached to a surgical robot. Driving torque of the surgical instrument is measured to estimate the interaction torque between the instrument tip and organ tissues. Friction occurring in the pulleys during torque transmission, however, induces estimation error. Coupling effect in the transmission structure also needs to be resolved for accurate estimation during multidegree- of-freedom motion. This paper proposes a method to reduce the estimation error by employing friction model in the multi-degreeof- freedom motion. The friction model is empirically developed based on analysis of the coupling effect and the characteristics of the driving mechanism. Experiments with right-grip motion in the multi-DOF show that the estimation error is reduced to 7.70 %.