Non-intrusive eye tracking plays an important role in many vision-based human computer interaction applications. How to ensure the robustness of external interference and tracking precision during eye tracking is the key problem to its applications owing to the strong nonlinearity of eye motion. To improve the robustness and precision of eye tracking, the Strong Tracking fifth-degree Cubature Kalman Filter(ST-5thCKF) algorithm is proposed. The algorithm introduces the suboptimal fading factor of Strong Tracking Filter(STF) into fifth-degree Cubature Kalman Filter(5thCKF) which almost has the least cubature sampling points while maintaining the fifth-degree filtering accuracy. The proposed algorithm bears the high filtering precision to strong nonlinearity of 5thCKF, as well as the robustness to external interference of STF. The experimental results under practical conditions show the validity of the proposed algorithm in eye tracking.