Haptic feedback is a critical but a clinically missing component in robotic Minimally Invasive Surgeries. This paper proposes a Gaussian Process Regression(GPR) based scheme to address the gripping force estimation problem for clinically commonly used elongated cable-driven surgical instruments. Based on the cable-driven mechanism property studies and surgical robotic system properties, four different Gaussian Process Regression filters were designed and analyzed, including: one GPR filter with 2-dimensional inputs, one GPR filter with 3-dimensional inputs, one GPR Unscented Kalman Filter (UKF) with 2-dimensional inputs, and one GPR UKF with 3-dimensional inputs. The four proposed methods were compared with the dynamic model based UKF filter on a 10mm gripper on the Raven-II surgical robot platform. The experimental results demonstrated that the four proposed methods outperformed the dynamic model based method on precision and reliability without parameter tuning. And surprisingly, among the four methods, the simplest GPR Filter with 2-dimensional inputs has the best performance.