The invention relates to a special strong combination column and combination beam frame with internally-arranged core columns and a construction method of the special strong combination column and combination beam frame. The special strong combination column and combination beam frame with the internally-arranged core columns is provided with internally-arranged asymmetric steel rib or plastic rib prestressed concrete combination beams and reinforcing bar concrete combination columns with the internally-arranged core columns, the combination beams are horizontally arranged between the combination columns, and the combination beams are connected with the combination columns at intersections through joints. The core columns are formed by pouring steel ribs or plastic ribs and concrete together, longitudinal ribs are distributed around the core columns and are wrapped by stirrups, and the core columns are placed in the reinforcing bar concrete columns. Transverse stiffening ribs are arranged on the steel ribs or the plastic ribs in the combination beams, the steel ribs or the plastic ribs at the midspan positions are arranged on the lower portions of the combination beams, the steel ribs or the plastic ribs on supports are arranged on the upper portions of the combination beams, and prestressed ribs are arranged in the combined beams in the length direction. The prestressed ribs on the beam and column joints penetrate through two sides of the core columns, and are tensioned and anchored at the ends of the combination columns. The axial pressure performance of the columns can be improved, the section size of the combination columns is small, the core columns can be poured on the scene and can also be prefabricated in factories, field mounting is achieved, workloads are reduced, and the construction period is shortened.