Projects are instrumental to the sustainable development of organisations and society. The integration of sustainability concepts into project management is also recognized as an important global project management trend. However, the practices do not reflect this role of projects and project management in sustainability. Therefore, the research reported in this paper studies how project managers perceive the contribution of project management to a more sustainable society, as an indication of the awareness that project managers have about their role in sustainable development. The study adopted grounded theory-based research based on qualitative data collection and analysis. The findings reveal that the sustainability theme is reasonably familiar to the project managers, though mainly in the meaning of sustainability of the project. The other meanings, sustainability by the project, sustainability of the organisation, and the project manager’s ethics and behaviour towards sustainability, were much less mentioned. The findings suggest that the project managers perceive the contribution of project management to a more sustainable society primarily related to the project processes and are less aware of the role projects play in changing organisations and society towards sustainability.