Being the language used in website designs, CSS is one of the language supported by Vim’s auto-complete feature.

To start using the feature, enter the following while in Vim’s command mode. 

:set omnifunc=csscomplete#CompleteCSS

That will enable CSS auto-completion in Vim. To use it, press Ctrl + x followed by Ctrl + o while partially typing CSS codes.

The following is a sample screenshot.

You can use the arrow key to navigate through the list to choose your desired auto-complete suggestion.