This paper deals with Discourse Argument Identification (DAI) from both intra-sentence and inter-sentence perspectives. For intra-sentence cases, we approach it via a simplified shallow semantic parsing framework, which recasts the discourse connective as the predicate and its scope into several constituents as the argument of the predicate. Different from state-of-the-art chunking approaches, our parsing approach extends DAI from the chunking level to the parse tree level, where rich syntactic information is available, and focuses on determining whether a constituent, rather than a token, is an argument or not. For inter-sentence cases, we present a lightweight heuristic rule-based solution. Evaluation using Penn Discourse Treebank (PDTB) shows that the current research’s parsing approach significantly outperforms the state-of-the-art chunking alternatives.