Complex two-dimensional (2D) photonic crystal (PC) constructed with a portion of 12-fold photonic quasicrystals (PQ) is proposed and its defect-mode properties are studied by performing finite-difference time-domain (FDTD). The results show that such complex PC allow for richer defect modes and higher degree of flexibility compared with conventional periodic PCs due to the absence of translational symmetry in the portion of 12-fold PQ. It is also demonstrated that the frequencies of defect modes are related to the strength of the interplay of the removed cylinders. The defect modes of flexibility and tunability can be obtained by combining different defect cavities.