The recommendation system has been widely used and studied in the last decade. The main purpose of a recommendation system is to generate relevant choices based on the user's preference for helping decision-making. The focus of this project is to propose a graph-based recommendation algorithm by analyzing the inner relationship between items and users’ preferences. Generally, in a graph-based recommendation system, users and items are nodes in the graph and edges represent the relationships. The recommendation problem is based on the following model, given n users, m items and users’ rating on items. The algorithm will find k relevant recommendations to the target user. The algorithm has the following steps: i) identify users’ preferences and simplify the rating scale, ii) create a graph-based recommendation system which represents the relationships between items. iii) based on the recommendation system calculate items’ Shannon entropy. iv) Using the recommendation system, recommend k items to the target user based on preference. v) filetering recommednations by Shannon entropy. The proposed algorithm tires to balance the diversity and precision of recommendations.