Let ( M , g , f ) (M, g, f) be a gradient Ricci soliton ∇ 2 f + R i c = λ g \nabla ^2 f+Ric=\lambda g with λ ∈ { 1 2 , 0 , − 1 2 } \lambda \in \{\frac {1}{2}, 0, -\frac {1}{2}\} . Suppose there is a geodesic line γ : ( − ∞ , ∞ ) → M \gamma : (-\infty , \infty )\rightarrow M satisfying lim inf t → ∞ ∫ 0 t R i c ( γ ′ ( s ) , γ ′ ( s ) ) d s + lim inf t → − ∞ ∫ t 0 R i c ( γ ′ ( s ) , γ ′ ( s ) ) d s ≥ 0 , \begin{eqnarray*} \liminf _{t\rightarrow \infty }\int _0^{t}Ric(\gamma ’(s), \gamma ’(s))ds +\liminf _{t\rightarrow -\infty }\int _{t}^{0}Ric(\gamma ’(s), \gamma ’(s))ds \geq 0, \end{eqnarray*} then ( M , g , f ) (M, g, f) splits off a line isometrically.