Knowledge-grounded Question Answering (QA) aims to provide answers to structured queries or natural language questions by leveraging Knowledge Graphs (KGs). Existing approaches are mainly divided into Knowledge Graph Question Answering (KGQA) and Complex Query Answering (CQA). Both approaches have limitations: the first struggles to utilize KG context effectively when essential triplets related to the questions are missing in the given KGs, while the second depends on structured first-order logic queries. To overcome these limitations, we propose a novel framework termed Aqua-QA. Aqua-QAapproximates query graphs from natural language questions, enabling reasoning over KGs. We evaluate Aqua-QA on challenging QA tasks where KGs are incomplete in the context of QA, and complex logical reasoning is required to answer natural language questions. Experimental results on these datasets demonstrate that Aqua-QA outperforms existing methods, showcasing its effectiveness in handling complex reasoning tasks in knowledge-grounded QA settings.