Existing partial sequence labeling models mainly focus on max-margin framework which fails to provide an uncertainty estimation of the prediction. Further, the unique ground truth disambiguation strategy employed by these models may include wrong label information for parameter learning. In this paper, we propose structured Gaussian Processes for partial sequence labeling (SGPPSL), which encodes uncertainty in the prediction and does not need extra effort for model selection and hyperparameter learning. The model employs factor-as-piece approximation that divides the linear-chain graph structure into the set of pieces, which preserves the basic Markov Random Field structure and effectively avoids handling large number of candidate output sequences generated by partially annotated data. Then confidence measure is introduced in the model to address different contributions of candidate labels, which enables the ground-truth label information to be utilized in parameter learning. Based on the derived lower bound of the variational lower bound of the proposed model, variational parameters and confidence measures are estimated in the framework of alternating optimization. Moreover, weighted Viterbi algorithm is proposed to incorporate confidence measure to sequence prediction, which considers label ambiguity arose from multiple annotations in the training data and thus helps improve the performance. SGPPSL is evaluated on several sequence labeling tasks and the experimental results show the effectiveness of the proposed model.