  We establish the Strassen's law of the iterated logarithm for independent and
identically distributed random variables with
$\hat{\mathbb{E}}[X_1]=\hat{\mathcal{E}}[X_1]=0$ and
$C_{\mathbb{V}}[X_1^2]<\infty$ under sub-linear expectation space with a
countably sub-additive capacity $\mathbb{V}$. We also show the LIL for upper
capacity with $\sigma=\bar{\sigma}$ under some certain conditions.
