A large number of electronic documents are labeled using human-interpretable annotations. High-efficiency text mining on such data set requires generative model that can flexibly comprehend the significance of observed labels while simultaneously uncovering topics within unlabeled documents. This paper presents a novel and generalized on-line labeled topic model (OLT) tracking the time development of extracted topics through a structured multi-labeled data set. Our topic model has an incrementally updated principle based on time slices in an on-line fashion, and can detect dynamic trending for labeled topics in parallel. Empirical results are presented to demonstrate lower perplexity and high performance of our proposed model when compared with other models.