Semantic role labeling (SRL) is a crucial task of natural language processing (NLP). Although generative decoder-based large language models (LLMs) have achieved remarkable success across various NLP tasks, they still lag behind state-of-the-art encoder-decoder (BERT-like) models in SRL. In this work, we seek to bridge this gap by equipping LLMs for SRL with two mechanisms: (a) retrieval-augmented generation and (b) self-correction. The first mechanism enables LLMs to leverage external linguistic knowledge such as predicate and argument structure descriptions, while the second allows LLMs to identify and correct inconsistent SRL outputs. We conduct extensive experiments on three widely-used benchmarks of SRL (CPB1.0, CoNLL-2009, and CoNLL-2012). Results demonstrate that our method achieves state-of-the-art performance in both Chinese and English, marking the first successful application of LLMs to surpass encoder-decoder approaches in SRL.