Closed-minded is the more logical spelling of the phrasal adjective meaning intolerant of others or unreceptive to new ideas. But close-minded is the more common spelling, and many dictionaries list it at least as a secondary form.
Closed-minded is logical because we wouldn’t say of an intolerant person that his mind is close, which would mean literally that his mind is near. Instead, we would say his mind is closed. Some dictionaries do list not open as one of the many adjectival definitions of close, but in actual 21st-century usage close usually gives way to closed for this sense. Still, logic rarely holds sway over English usage.
While close-minded has the edge, both forms are easily found in current news and blog writing—for example:
[T]hose who hold conservative political views are more likely to be closed-minded, conformist and resistant to change. [Washington Post]
After breaking parole, Jean is pursued by Javert, Russell Crowe’s unremittingly close-minded policeman. [NJ Today]
It is rather closed-minded to start wringing our hands at the lack of American gun control. [Telegraph]
What terrifies me is that my kids will come out of their schools as fearful, close-minded, ignorant ninnies. [Washington Times Communities]
A leader who comes from a Christian tradition … runs the risk of looking sectarian and closed-minded by hanging out with fellow believers. [Globe and Mail]