In this paper we demonstrate a method for estimating asymptotic behavior of the regularly varying moments $E(K_\rho (X_n))$, $(n\to\infty)$ in the case of generalized Binomial Law. Here $K_\rho(x)$ is from the class of regularly varying functions in the sense of Karamata. We prove that $$ E(K_\rho(X_n))\sim K_\rho(E(X_n)), \rho>0, E(X_n)\to\infty (n\to\infty), $$ i.e., that the asymptotics of the first moment determines the behavior of all other moments.