The invention relates to a stepped palace inner and outer finned tube for both evaporation and condensation, including a tube base, a spiral sawtooth inner fin, a spiral sawtooth outer fin, inter-slot convex teeth, a palace lattice fin, a stepped fin, and a triangular top tooth. The grid fins are located on both sides of the spiral serrated outer fins, and the grid fins on both sides of the same spiral serrated outer fin are alternately distributed; the stepped fins are located on both sides of the spiral serrated outer fins and are located outside the grid fins. The stepped fins on both sides of the same spiral serrated outer fin are alternately distributed, and the stepped fins on the same side are alternately distributed with the grid fins; the inner side of the grid fins, the spiral serrated outer fins, the tube base, and the convex teeth An evaporation chamber is enclosed between them, and an intensified chamber is enclosed between the outer side of the grid fins, the spiral sawtooth outer fins, and the stepped fins, and the evaporation chamber and the intensified chamber are connected through gaps. The invention can improve the heat transfer efficiency of two working conditions of evaporation and condensation, and belongs to the technical field of enhanced heat transfer tubes.