In a lower vehicle-body structure of a vehicle, there is provided a rear connecting member swingably supporting a rear portion of a lower arm at a sub frame and a front side frame, the rear connecting member comprising a support portion to support the lower arm, a fifth connection portion to connect the sub frame and the support portion, and a fourth connection portion to connect the front side frame and the support portion. Further, there is provided a separation mechanism to separate the fourth connection portion off the front side frame in the vehicle frontal collision. Accordingly, the sub frame and the lower arm are separated off the front side frame by the separation mechanism.