Complex analysis is a very important branch of Mathematics and lot of works has been done in this field. One of the important part is growth analysis of entire and meromorphic functions. The ratio $\frac{M_{f}(r)}{M_{g}(r)}$ is called the growth of the entire function $f$ with respect to entire function $g$ in terms of maximum modulus functions. Order and type are classical growth indicators. Definitions of order and type of entire and meromorphic functions have been extended several times. Recently, Bela\"{\i}di et al. [1] have extended the previous ideas and have introduced the definitions of $(\alpha ,\beta ,\gamma )$-order of entire and meromorphic functions. The generalized definitions of order of entire function are obtained by some researchers in terms of central index (see [2, 3]). In this paper, we have discussed on central index oriented some growth properties of composite entire functions on the basis of their $(\alpha ,\beta ,\gamma )$-order and $(\alpha ,\beta ,\gamma )$-lower order, and have generalized some previous works in this line.