High-utility itemset mining is one of the highly researched area. Many research enthusiasts have discovered various techniques and algorithms to mine high-utility itemsets from transaction databases. One of the limitations of the existing high-utility itemset mining techniques is that there is no any generalized framework for applying the custom combinations of input parameters and any other constraints for mining high utility itemsets. This paper proposes a novel customizable framework to discover customized high utility itemsets (C-HUI). Users can customize the constraints and/or input parameters as per their requirements. A novel C-HUIM algorithm is used to discover customized high utility itemsets (C-HUI) from real-life datasets. The experimental results of the proposed framework and C-HUIM algorithm highlight the effectiveness of the approach.