This paper describes the development of an agile project management system. This research is relevant because of the feature of agile projects consisting of changing requirements. We developed the architecture of the backlog and tasks management system, including a duration prediction module. Using the developed system, managers have the opportunity to divide project processes into sprints depending on the prediction and value for the stakeholders. The authors propose a method for predicting agile project duration by formalising the application of expert Story Point evaluation and subsequent Monte Carlo simulation. Based on the developed method, an algorithm for the dynamic prediction of task duration was designed. Integration of the developed method into the system made it possible to reduce the assumptions and limitations associated with updating user story data and participation in the projects of new and cross-functional teams. The developed system allows managers to cope with agile project bottlenecks.