Checking grammar using a computer program has indeed turned out to be much harder than computer scientists thought when the computer was a new concept. Some even thought natural language, logic, and all the rest would be something the computer would be able to deal with in a jiffy.
I think computer science has contributed to language studies the fact that language is way more complex than a simple algorithm.
That being said, Grammarly is a tool that will grammar check English and it has a free edition. (ProWritingAid is another tool, but I haven't looked into it much—it does seem to have a free edition though).
Is Grammarly any good? It does help me find small problems when I write, however, more importantly, it will do this by forcing my text into their cookie-cutter idea of a grammatically correct text.
And yes, Grammarly does sometimes get the grammar wrong and suggests things that don't seem right...
I would never, ever, use Grammarly (or any other tool) for anything but blog posts, texts on places like Writing.SE, and work-related texts in English.
For fiction (even if I wrote in English) I'd rely on beta readers, editors, and so on... Never a program... mainly because, as I mentioned, you might lose your style and voice if your English will be forced into their idea of good language.