In this paper authors give a nice application of hypergeometric matrix function in geometric function theory. Hypergeometric matrix function was earlier studied by Jodar and Cortes and have a great importance in special functions. Hypergeometric matrix function is analogues to hypergeometric function. Although, the application of hypergeometric matrix function is not explored in G. F. T. In the present paper we attempt to fill this gap by giving a nice application of hypergeometric matrix function. The main purpose of the present article is to obtain some sufficient conditions for the hypergeometric matrix function belonging to certain classes of starlike and convex functions. We obtain these conditions by applying coefficient conditions of starlike and convex functions studied by Silverman in 1975. Finally, we discuss an integral operator associated with this function. The results of this paper are quiet ne and interesting. This paper opens up a new and interesting direction of research in geometric function theory.