As exceedingly rare heresy, this teaching is named after its founder, Apollinaris of Laodicea. A subset of the wider Arian heresy, this teaching is that Jesus did not have a human mind, denying the hypostatic union and the two-fold nature of Christ as being both completely man and completely God. This teaching was meant to counter Arius, who taught that Jesus was not divine. However, this created an altogether diffeent heresy, diminishing the humanity of the 2nd Person of the Trinity.
This view was condemned as heresy at the Synod of Alexandria (AD 362).
Modern practitioners are few, but some make the case that William Lane Craig is a neo-Apollinarian because of certain statements he has made in regard to the nature of Christ.