The new quasi-square honeycomb is one kind of transitional form of hexagonal honeycomb. It is of great significance to study its equivalent elastic parameters and vibration characteristics. The differences of the in-plane equivalent elastic parameters between the quasi-square honeycomb core with the double wall thickness and equal wall thickness were analyzed through the revised Gibson formulas. And the vibration performance of all edges simply supported quasi-square honeycomb sandwich structure with two different wall thickness under the influence of different equivalent elastic parameters was analyzed through the classic laminate theory. A finite element model of the quasi-square honeycomb sandwich structure with different wall thickness was presented to analyze its vibration characteristics, and the simulation results were compared with the theoretical analysis results. The results showed that the numerical simulation results of equivalent elastic parameters were basically in agreement with the theoretical values. Under the same basic structure parameters of the honeycomb, the in-plane equivalent shear modulus, out-plane stiffness and equivalent density of the quasi-square honeycomb core with double wall thickness were larger than those of the quasi-square honeycomb core with equal wall thickness. The natural frequencies of the quasi-square honeycomb sandwich structure with double wall thickness was lower than that of the honeycomb with equal wall thickness in the low-order vibration mode and higher in the high-order vibration mode. The influence of the three main impact factors on the natural frequency of the sandwich structure were listed in descending order as the yoz-plane equivalent shear modulus, the equivalent density and the wall thickness of the quasi-square honeycomb core. Study results indicat that the natural frequency of the quasi-square honeycomb sandwich structure calculated by the classic laminate theory has preferably coherence with the numerical simulation results. The correctness of the equivalent elastic parameters of the quasi-square honeycomb sandwich core obtained by the modified Gibson formula is further proved. This vibration theory is extended to the feasibility of calculating the general honeycomb sandwich structure, which lays a foundation for expanding the vibration characteristics of other types of honeycomb sandwich structures.