Knowledge Graph Question Answering (KGQA) aims to answer natural language questions over Knowledge Bases. Information Retrieval Based methods usually contain two stages: question-specific subgraph retrieval and answer reasoning. Most recent methods focus on the relevance between retrieved entities or relations and questions, which often results in excessively large subgraphs, making it difficult for graph neural networks to effectively reason. Since Large Language Models (LLMs) demonstrate exceptional capabilities in understanding complex natural language queries, we propose LQRPP-KGQA, a novel approach that leverages LLMs to predict question-specific reasoning paths and enhance reasoning over subgraphs. Specifically, we present a retrieval-predict-expansion-reason framework, where it first retrieves valid reasoning paths from the Knowledge Bases to conduct instruction fine-tuning. Furthermore, we define several reasoning sub-paths to prompt the fine-tuned LLMs to predict potential sub-paths, which are then expanded into question-specific subgraphs. Finally, we leverage graph neural networks to perform reasoning over these enriched subgraphs. We conduct KGQA experiments on two widely used datasets to validate its functionality. Extensive experiments on two benchmark KGQA datasets demonstrate that LQRPP-KGQA achieves competitive performance on KGQA tasks.