What steps are you taking to delete the project, and what happens when you try?
The project delete process is to open the projects browser (where your projects are displayed as icons), and then move your cursor over the project icon to reveal a little circle with dots in it to the right of the title. When you click on the circle, a drop down menu will display an option to delete the project. If you want to permanently remove from your iMovie library the media that is contained in the project, then after deleting the project you need also to delete the Event in the media sidebar that bears the project's name. When you delete the project a message box will appear to notify you of that. However, be aware that deleting the project media event will remove the media from all other projects that may be accessing it, as well as permanently deleting it from you iMovie library.
If you are doing the above and still the project won't delete, then try deleting preferences and see if that will cure the problem. Open iMovie while holding down the Option and Command keys and select to delete preferences in the box that appears.
iMovie will open in a new library. Reopen your old library to get back to your projects. Deleting preferences is a safe procedure that will not cause data loss or disruption to your project.
-- Rich