1. be unwilling to entertain or accept new ideas or beliefs, be averse to challenging your preconceptions
a closed-minded person is difficult to deal with
Unlike the expression '(keep/have) an open mind', you wouldn't really instruct someone to 'keep' a closed mind, as this is generally seen as a negative trait. However, you can say that someone keeps or kept a closed mind. Generally speaking, a person who is unwilling to listen to anyone talk about other possibilities or truths - especially in relation to religion or science - is said to be closed-minded. Although the phrasal adjective 'closed-minded' - describing someone's behaviour - is correct and makes more sense, you will often see it spelled 'close-minded'. This expression is not as popular as its antonym (opposite) '(keep/have) an open mind', as most English speakers would describe a closed-minded person by saying they are 'not very open-minded'.