  We consider a $q$-Painlev\'e IV equation which is the $A_4^{(1)}$-surface
type in the Sakai's classification. We find three distinct types of classical
solutions with determinantal structures whose elements are basic hypergeometric
functions. Two of them are expressed by ${}_2\varphi_1$ basic hypergeometric
series and the other is given by ${}_2\psi_2$ bilateral basic hypergeometric
series.
