Please don't delete projects that have any work history that you will later regret losing. Deleted items and objects (projects) cannot be recovered.
Once you're certain that you want to delete a project, you will need to change the project "State" into the setting "To Be Deleted." Without that setting, the project cannot be deleted. This is a safety mechanism unique to Project objects to prevent the loss of important historical information, including the details as to the time and money resources spent on the project.
If the above answer does not work, it might be because you do not have delete permissions to the project. Your PI administrator needs to grant delete permissions which are usually managed at the folder level within which the project is contained.