Two types of triangular gradient rib honeycombs (Triangular gradient rib honeycomb-Type Z-AXBYs) were designed and proposed in this paper. A finite element numerical model was constructed using Abaqus/Explicit, with model accuracy verified, and a series of studies were conducted. Firstly, the mechanical properties of TCH, TGH, and two types of TGRH-Type Z-AXBYs under axial impact were analyzed. Results showed that the specific energy absorption (SEA) of TGH improved by 101.27% compared to TCH; TGRH-Type I-170°-AXBYs SEA improved by up to 77.21% compared to TGH; TGRH-Type II-180°-AXBYs SEA improved by up to 63.84% compared to TGH. Adding a layer with a larger angle at the bottom of the honeycomb effectively improved the impact resistance and energy absorption of the structure. The mechanical properties of two types of TGRH-Type Z-θ-AXBYs with different layers were studied, showing that TGRH-Type I-θ-AXBYs had the best mechanical properties. TGRH-Type I-θ-AXBYs SEA improved by a maximum of 23.57% compared to TGRH-Type II-θ-AXBYs and by a minimum of 13.71%. TGRH-Type I-θ-AXBYs SEA improved by a maximum of 74.95% and a minimum of 12.88% compared to TGRH-Type I-θ-6X. Finally, the effects of wall thickness and velocity on the two types of TGRH-Type Z-AXBYs were analyzed. Properly increasing the wall thickness effectively improved the impact resistance of the structure. This paper provides a feasible reference for introducing a gradient ribbed plate design into triangular honeycombs to enhance their in-plane mechanical properties.