The state of health for lithium battery is necessary to ensure the reliability and safety for battery energy storage system. Accurate prediction battery state of health plays an extremely important role in guaranteeing safety and minimizing the maintenance costs. However, the complex physicochemical characteristics of battery degradation cannot be obtained directly. Here a novel Gaussian process regression model based on partial incremental capacity curve is proposed. First, an advanced Gaussian filter method is applied to obtain the smoothing incremental capacity curves. The health indexes are then extracted from the partial incremental capacity curves as the input features of the proposed model. Otherwise, the mean and the covariance function of the proposed method are applied to predict battery state of health and the model uncertainty, respectively. Four aging datasets from NASA data repository are employed for demonstrating the predictive capability and efficacy of the degradation model using the proposed method. Besides, different initial health conditions of the tested batteries are used to verify the robustness and reliability of the proposed method. Results show that the proposed method can provide accurate and robust state of health estimation.