Purpose: This study aims to investigate the relationship between nonverbal cognitive functions and language processing of people with aphasia (PWA) by taking a data-driven approach, as well as multiple cognitive components and multilevel linguistic perspectives. It is hypothesized that language performance is differentially associated with cognitive processing of PWA, with executive functions (EFs) playing a stronger role in language tasks with increasing linguistic complexity. Method: A language battery assessing word comprehension/production, sentence comprehension, and discourse production, together with a series of non-linguistic cognitive tasks targeting simple/complex attention, short-term/working memory, or EFs, was administered to 53 Cantonese-speaking PWA. Cognitive factors extracted from principal component analysis applied to the cognitive battery served as predictors in four multiple regression analyses to predict PWA’s performance at various linguistic levels. Results: Two cognitive factors, representing (a) simple attention and memory and (b) EF, were extracted. The former predicted performance in word processing tasks, whereas EF significantly predicted performance in all language tasks with increasing contribution as a function of linguistic complexity. Conclusion: The results based on Chinese PWA provide comprehensive evidence for the view that language performance is the end product of interaction between linguistic and nonlinguistic functions and have clear implications for clinical management of PWA.