Class imbalance in data presents significant challenges for classification tasks. It is fairly common and requires careful handling to obtain desirable performance. Traditional classification algorithms become biased toward the majority class. One way to alleviate the scenario is to make the classifiers cost-sensitive. This is achieved by assigning a higher misclassification cost to minority-class instances. One issue with this implementation is that all the minority-class instances are treated equally, and assigned with the same penalty value. However, the learning difficulties of all the instances are not the same. Instances that are located in the overlapping region or near the decision boundary are harder to classify, whereas those further away are easier. Without taking into consideration the instance complexity and naively weighting all the minority-class samples uniformly, results in an unwarranted bias and consequently, a higher number of misclassifications of the majority-class instances. This is undesirable and to overcome the situation, we propose a novel instance complexity-based cost-sensitive approach (termed 'iCost') in this study. We first categorize all the minority-class instances based on their difficulty level and then the instances are penalized accordingly. This ensures a more equitable instance weighting and prevents excessive penalization. The performance of the proposed approach is tested on 65 binary and 10 multiclass imbalanced datasets against the traditional cost-sensitive learning frameworks. A significant improvement in performance has been observed, demonstrating the effectiveness of the proposed strategy.