Semantic role labeling (SRL) is to recognize the predicate-argument structure of a sentence, including subtasks of predicate disambiguation and argument labeling. Previous studies usually formulate the entire SRL problem into two or more subtasks. For the first time, this paper introduces an end-to-end neural model which unifiedly tackles the predicate disambiguation and the argument labeling in one shot. Using a biaffine scorer, our model directly predicts all semantic role labels for all given word pairs in the sentence without relying on any syntactic parse information. Specifically, we augment the BiLSTM encoder with a non-linear transformation to further distinguish the predicate and the argument in a given sentence, and model the semantic role labeling process as a word pair classification task by employing the biaffine attentional mechanism. Though the proposed model is syntax-agnostic with local decoder, it outperforms the state-of-the-art syntax-aware SRL systems on the CoNLL-2008, 2009 benchmarks for both English and Chinese. To our best knowledge, we report the first syntax-agnostic SRL model that surpasses all known syntax-aware models.