Question answering systems may find the answers to users' questions from either unstructured texts or structured data such as knowledge graphs. Answering questions using supervised learning approaches including deep learning models need large training datasets. In recent years, some datasets have been presented for the task of Question answering over knowledge graphs, which is the focus of this paper. Although many datasets in English were proposed, there have been a few question-answering datasets in Persian. This paper introduces \textit{PeCoQ}, a dataset for Persian question answering. This dataset contains 10,000 complex questions and answers extracted from the Persian knowledge graph, FarsBase. For each question, the SPARQL query and two paraphrases that were written by linguists are provided as well. There are different types of complexities in the dataset, such as multi-relation, multi-entity, ordinal, and temporal constraints. In this paper, we discuss the dataset's characteristics and describe our methodology for building it.