A variable-magnification projection optical system substantially consists of a negative first lens group that is disposed at the most enlargement-side position and is fixed during magnification change, a positive last lens group that is disposed at the most reduction-side position and is fixed during magnification change, and a plurality of lens groups that are disposed between the first lens group and last lens group and are moved during magnification change. The most enlargement-side lens group (the second lens group) of the lens groups that are moved during magnification change has a negative refractive power. Predetermined conditional expressions relating to a back focus of the entire system on the reduction side at the wide-angle end, a focal length of the entire system at the wide-angle end, a focal length of the second lens group and a focal length of the last lens group are satisfied.