Dropbox will occasionally use around 100% of the CPU. Why is this happening and how do I fix it?
From searching around, it seems like it's not an uncommon problem.
Taken from this Ask Ubuntu question:
So it seems that the only way to fix it, will be to reduce the size of your shared Dropbox folder.
I have found solution here: http://www.michaelcarwile.com/throttle-dropbox-and-other-app-cpu-usage/
Get Dropbox’s Process ID:
Run cpulimit with the -p flag using the process ID: