We found that core-shell gyromagnetic photonic crystal of two-dimensional triangular lattice exhibit topological phases. In a certain parameters and magnetic field, those phases could be a conventional insulator phase, a quantum spin Hall phase, and a quantum anomalous Hall phase. Different from the structure of Ref[1], phase transitions in our core-shell structure does not involve changes of space symmetry, which depend on parameters of our structure and the broken of time reverse symmetry. Our result shows the variety of topological phase transitions in photonic crystals.