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We study the asymptotic volume ratio of non-steady gradient Ricci solitons.Moreover, a local estimate of the volume ratio is obtained for expandingsolitons which satisfy $\lim_{dist(O,x)\rightarrow\infty} |Sect|\cdotdist(O,x)^2=0$. Therefore, for such a soliton, we can show that it must have$\mathbb{R}^n$ as one of its tangent cone at infinity. (Here we assume that thesoliton is simply connected at infinity, has only one end and $n\geq 3$.)

Volume estimates and the asymptotic behavior of expanding gradient Ricci solitons