In my experience, lines around a mesh can often be caused by jagged edges and Smooth shading. See my answer here.
I assume you have Smooth Shading on, as activated in the Toolshelf. If you do, either return to Flat Shading or add a Subdivision surface object modifier.
To add such a modifier, first go to the Object Modifiers tab in the Properties panel. Select Subdivision surface from the options. Set both the View: value to 2 and the Render: value to 3.
Final modifier settings:
Smooth shaded Suzanne without any subsurf:
Smooth shaded Suzanne with subsurf at 3:
Flat shaded Suzanne: