The invention relates to a vehicle-body lower structure of a vehicle. A cross member 7 extending along the vehicle width direction is provided between a tunnel portion 5 and a connection portion of the center pillar 4 connected to a side sill 2. The vehicle-body lower structure includes a connection member 12 connecting the outside portion of the cross member 7 and an inside wall face portion 11 of the side sill 2, wherein the connection member 12 includes the cross-member-side connection portion connected to the cross member 7 and a side-sill-side connection portion connected to the side sill 2, the side-sill-side connection portion is configured to have the lower rigidity than the cross-member-side connection portion, and the outside end portion of the cross member 7 is located at the specified position which is located on the outside of the cross-member-side connection portion and on the inside away from the inside wall face portion of the side sill 2. Thereby, the impact load in the vehicle side collision can be effectively supported by the cross member with a simple structure.