A Firefly Algorithm (FA) is an effective and powerful metaheuristic algorithm that is primarily proposed for solving continuous optimization problems. However, since FA has attractive properties like stability, high convergence characteristics, and easy implementation, several studies have been worked on for modifying FA to accommodate discrete or binary domain problems. By this work, a new revised firefly technique to mine association rules, named Modified Firefly Algorithm accomplishing Association Rules Mining (MFA-ARM), is proposed with significant modifications that have been applied to the original version of FA in order to handle properly regarding the issue of mining association rules. A core modification presented in the proposed algorithm is the new movement technique, which regulates the traveling of fireflies toward the most attractive one. The performance of the MFA-ARM algorithm was tested against three well-known data-sets and compared with the performance of the recently developed metaheuristic, the DCS-ARM algorithm. The experimental results expressed that the performance of the new proposed technique (MFA-ARM) is nearby to that of the DCS-ARM technique since both of the metaheuristic algorithms discover high quality rules with good confidence and support values. Nevertheless, the main difference in the performance of the two algorithms is in the size of the rules extracted by them. Hence, the results proved that the proposed MFA-ARM algorithm discovers rules with a smaller size than those extracted using the DCS-ARM algorithm in the three data-sets. Moreover; these rules are more understandable and easier to interpret. The results revealed that the MFA-ARM algorithm has a somewhat quicker execution time than that of the DCS-ARM algorithm in all experimented data-sets. However, some of MFA-ARM algorithm steps are only suitable for discrete data.