A vehicle-body structure for an electric vehicle including a traveling motor, the vehicle-body structure comprising: a battery unit including a battery frame and a battery (FD, RD) that supplies electric power to the traveling motor, the battery frame being disposed below a vehicle cabin and extending in a vehicle front-rear direction, wherein a battery housing portion (200, 201) in which the battery is housed and a battery non-housing portion in which the battery is not housed are provided alongside in a vehicle front-rear direction below the vehicle cabin, wherein the battery housing portion includes a front-side battery housing portion provided on a vehicle front side of the battery non-housing portion, and a rear-side battery housing portion provided on a vehicle rear side of the battery non-housing portion, and the battery frame includes a first frame portion (16, 17, 19) including front-side and rear-side first frame portions (16, 17) disposed at said front-side and rear-side battery housing portions (200, 201) of the battery housing portion, and a second frame portion disposed at the battery non-housing portion, characterized in that said first frame portion (16, 17, 19) includes one or more central members (16, 17, 19) extending in the front rear direction inside the battery housing portion (200, 201) of the battery frame and said second frame portion includes a central member extending in the front rear direction inside the battery non-housing portion of said battery frame, wherein said central member of the second frame portion is larger in width than said central member of the first frame portion in a vehicle width direction. a battery unit including a battery frame and a battery (FD, RD) that supplies electric power to the traveling motor, the battery frame being disposed below a vehicle cabin and extending in a vehicle front-rear direction, wherein a battery housing portion (200, 201) in which the battery is housed and a battery non-housing portion in which the battery is not housed are provided alongside in a vehicle front-rear direction below the vehicle cabin, wherein the battery housing portion includes a front-side battery housing portion provided on a vehicle front side of the battery non-housing portion, and a rear-side battery housing portion provided on a vehicle rear side of the battery non-housing portion, and the battery frame includes a first frame portion (16, 17, 19) including front-side and rear-side first frame portions (16, 17) disposed at said front-side and rear-side battery housing portions (200, 201) of the battery housing portion, and a second frame portion disposed at the battery non-housing portion, characterized in that said first frame portion (16, 17, 19) includes one or more central members (16, 17, 19) extending in the front rear direction inside the battery housing portion (200, 201) of the battery frame and said second frame portion includes a central member extending in the front rear direction inside the battery non-housing portion of said battery frame, wherein said central member of the second frame portion is larger in width than said central member of the first frame portion in a vehicle width direction.