Due to the narrow space and a harsh chemical environment in the sterilization processes for the end-effector of surgical robots, it is difficult to install and integrate suitable sensors for the purpose of effective and precise force control. This paper presents an innovative tension sensor for estimation of grasping force in our laparoscope surgical robot. The proposed sensor measures the tension of cable using fiber gratings (FBGs) which are pasted in the grooves on the inclined cantilevers of the sensor. By exploiting the stain measurement characteristics of FBGs, the small deformation of the inclined cantilevers caused by the cable tension can be measured. The working principle and the sensor model are analyzed. Based on the sensor model, the dimensions of the sensor are designed and optimized. A dedicated experimental setup is established to calibrate and test the sensor. The results of experiments for estimation the grasping force validate the sensor.