In this paper, we propose ZeFaV - a zero-shot based fact-checking verification framework to enhance the performance on fact verification task of large language models by leveraging the in-context learning ability of large language models to extract the relations among the entities within a claim, re-organized the information from the evidence in a relationally logical form, and combine the above information with the original evidence to generate the context from which our fact-checking model provide verdicts for the input claims. We conducted empirical experiments to evaluate our approach on two multi-hop fact-checking datasets including HoVer and FEVEROUS, and achieved potential results results comparable to other state-of-the-art fact verification task methods.