  In string theory, an important challenge is to show if the big-bang
singularity could be resolved by the higher derivative $\alpha'$ corrections.
In this work, based on the Hohm-Zwiebach formula, we construct a series of
non-singular non-perturbative cosmological solutions with the complete
$\alpha^{\prime}$ corrections, for the bosonic gravi-dilaton system. In the
perturbative regime, these solutions exactly match the perturbative results
given in literature. Our results show that the big-bang singularity indeed
could be smoothed out by the higher derivative $\alpha'$ corrections.
