Existing disambiguation strategies for partial structured output learning just cannot generalize well to solve the problem that there are some candidates which can be false positive or similar to the ground-truth label. In this paper, we propose a novel weak disambiguation for partial structured output learning (WD-PSL). First, a piecewise large margin formulation is generalized to partial structured output learning, which effectively avoids handling large number of candidate structured outputs for complex structures. Second, in the proposed weak disambiguation strategy, each candidate label is assigned with a confidence value indicating how likely it is the true label, which aims to reduce the negative effects of wrong ground-truth label assignment in the learning process. Then two large margins are formulated to combine two types of constraints which are the disambiguation between candidates and non-candidates, and the weak disambiguation for candidates. In the framework of alternating optimization, a new 2n-slack variables cutting plane algorithm is developed to accelerate each iteration of optimization. The experimental results on several sequence labeling tasks of Natural Language Processing show the effectiveness of the proposed model.