In this paper, we give an estimate on the difference between $x^n(t)$ and x(t) and it clearly shows that one can use the Picard iteration procedure to the approximate solutions to stochastic functional differential equations with infinite delay at phase space BC(($-{infty}$, 0] : $R^d$) which denotes the family of bounded continuous $R^d$-valued functions ${varphi}$ defined on ($-{infty}$, 0] with norm ${parallel}{varphi}{parallel}={sup}_{-{infty}<{ heta}{leq}0}{mid}{varphi}({ heta}){mid}$ under non-Lipschitz condition being considered as a special case and a weakened linear growth condition.