Generally speaking, a one-dimensional system requires chiral or particle-hole symmetry to be topologically nontrivial. In this Letter, we show that topological behavior can also be observed in a quasi-one-dimensional photonic system without the aforementioned symmetries. The results indicate that the quantized Zak phase is achieved in such a system even though the chiral and particle-hole symmetries are still absent. Further study shows that the system can support a topologically protected asymmetric near-zero mode on the right edge. Our work enriches the concepts of design of topological photonics and may have important applications in future quantum computations. (C) 2019 Optical Society of America