OpenOffice 3.4 only has a menu link for a grammar checker, it does not include one. So, if you have a grammar checker that claims to work with OpenOffice, you can install it and it will run after the Spell checker. However, all the English grammar checkers that support OpenOffice seem either so limited as to be useless, or in the case of one - positively damaging - read the comments before installing.
I have proof-read literally hundreds of books in English, and run my finished documents through the MS Office grammar checker before sending them off. That is pretty good at picking up the sort of trivial mistakes that come from boredom! I have tested several commercial grammar checkers and find that the MS Office one is the best. But, even that tool is not good as a first check; you must proof-read manually first, using your knowledge of English, and then use the grammar checker. I'm afraid a computer can't correct bad English reliably. If you don't know a language well, a grammar checker could even make things worse, and you would never know!