The morphologies and the phase diagram of comb copolymer A(m+1)(BC)(m) are investigated by the self-consistent field theory. By changing the volume fractions of the blocks, the interaction parameters between the different blocks, and the side chain number, nine phases are found, including the two-colored lamellar phase, three-colored lamellar phase, hexagonal lattice phase, core shell hexagonal lattice phase, two interpenetrating tetragonal lattice, core shell tetragonal lattice, lamellar phase with beads inside, lamellar phase with alternating beads, and disordered phase. The phase diagrams are constructed for A(m+1)(BC)(m) with different side chain numbers of m = 1, 2, 3, and 5. Due to the asymmetric topology of comb copolymer A(m+1)(BC)(m) the phases and the diagrams are very different from linear ABC triblock copolymer or star ABC triblock copolymer. When the volume fraction of one of the blocks is the domination, the (core shell) hexagonal phase or two interpenetrating tetragonal lattice can form, depending on which block dominates and the interaction between the blocks. The (core shell) hexagonal phase easily forms at the corner of the block A (f(A) >= 0.5). The side chain number in affects the phase diagram largely due to the fact that the architecture of a comb copolymer is not invariant under the interchange between the three different monomers. Due to the connectivity of the blocks B and the inner blocks A(m+1)(BC)(m). comb copolymers with the longer main chain A or longer side chain with short block C, i.e., longer block B, are difficult to phase separate. The results are helpful to design nano- or biomaterials with complex architecture or tailor the phase behavior of comb copolymers.