Ranking fuzzy numbers plays a very important role in the decision process, data analysis, and applications. The last few decades have seen a large number of methods investigated for ranking fuzzy numbers. The most commonly used approach for ranking fuzzy numbers is ranking indices based on the centroids of fuzzy numbers. However, there are some weaknesses associated with these indices. This paper reviews several fuzzy number ranking methods based on centroid indices and proposes a new centroid-index ranking method that is capable of effectively ranking various types of fuzzy numbers. The contents herein present several comparative examples demonstrating the usage and advantages of the proposed centroid-index ranking method for fuzzy numbers.