I'd say "to complete a circumnavigation" of the globe. But the verb is commoner: to circumnavigate the globe.

To undertake a circumnavigation is another possibility.

thank you so much!!

Just to be clear, I don't think 'do a circumnavigation' is grammatically wrong, it's just a slight mismatch because 'do' is casual and 'circumnavigation' is formal.

Is countable really the most common? I might go for something more like

Circumnavigation of the globe is now far easier than it once was, but it still requires solid knowledge of sailing and geography.

And I would say "Circumnavigating the globe is ..." :-)

I don't know what is more common, but you can certainly find lots of examples of a ... circumnavigation in the British press, which seems to like that kind of thing.

youngest person to complete a solo circumnavigation of the world

after a global circumnavigation

a 69-day circumnavigation of the continent

Joyon’s record for a solo circumnavigation marks not just ...

http://www.timesonline.co.uk/tol/sitesearch.d...

(BTW the OP specified that a solution using the noun was required.)