Delays in project delivery have become a common phenomenon in the project management profession. This should not be accepted as a norm considering that projects form an integral part of achieving an organization’s strategic objectives. This paper examines how internal organizational processes affect the successful delivery of projects by exploring a case study on the project management processes at a South African university. Managers in the university under the Operations Department were interviewed. The paper addresses project planning processes, organizational strategic objectives in relation to project management processes and reviews organizational bureaucracy and its effects on project processes. Furthermore, the analysis addresses current internal challenges through the Theory of Constraint. The findings provide insight to top management of various institutions who seek to improve their organizational project delivery system.