I'm an EU citizen and I'm married to a Chinese woman. Currently we live in the UK, and my wife wants go back home to see her family almost every year. Each time when we travel there, I need to apply for a visa. On the other hand, if we want to travel around Europe, she does not need a visa, as I hold a Schengen passport.
I wonder if there's something similar in China which allows me to enter China to travel around with my wife without a visa.
To the best of my knowledge there is no such thing.
While you can visit China visa-free either
this is not related to your status as a spouse of a Chinese national and you have made clear in comments that this not what you are looking for.
Then, for a visit you need a visa, either as a tourist (L) or family reunion (Q). User @BurhanKhalid also pointed out this sort of residence permit for family but as I read it that is not much use to you as it would need to be renewed annually and still is some sort of a visa.
Finally do note that, as has been pointed out in comments,
her not needing a visa is related to your very specific status as an EU citizen in the UK (and she does need a special document, her residence card, to enter EU countries). In all other cases (spouse of a British citizen in the UK, spouse of an EU citizen - even from a Schengen country - living outside the EU), Chinese citizens do need a visa.
