Most of the information technology (IT) projects are canceled or failed due to different reasons, while some of them are performed poorly in terms of cost, time, scope, customer satisfaction, etc. Therefore, it is important to identify the most important criteria affecting the performance of IT projects, measure their performance, identify the issues, and continually improve the performance of both the projects and the organizations. Although IT organizations place value on the importance of the project performance to release on time, with low cost, and in accordance with the customer expectations, they lack ways of determining the most suitable performance criteria for continually measuring, improving, and controlling them. This study proposes a new methodology to evaluate the performance of IT projects in a fuzzy environment. For this aim, firstly, the most suitable criteria are identified based on the balanced scorecard method. In the second step, the relative priorities of the criteria are determined with the help of expert judgments and hesitant fuzzy weights with hesitant multiplicative geometric operator. Then, the priorities of the criteria are used to evaluate the performance of IT projects in a Turkish company by using real data.