In recent years, metallic bar dampers have been widely applied in structural vibration reduction due to their excellent energy dissipation capacity. To further enhance the mechanical performance of metallic bar dampers, this study proposes a double hourglass-shaped damper made of LYP160 low-yield-point steel, featuring a constant cross-section straight segment LYP160-double hourglass shaped steel damper(LYP-DHSD). To investigate the mechanical properties of LYP-DHSD under shear displacement, two LYP-DHSD specimens were designed. The hysteretic characteristics and fatigue performance of the specimens were studied through low-cycle reciprocating loading tests. A refined finite element model of LYP-DHSD was developed, and parameter analysis of the hysteretic performance was conducted with the outer diameter, inner diameter, and length of the constant cross-section straight segment as variables to further explore the stress pattern of LYP-DHSD under cyclic shear displacement. The results show that under cyclic shear displacement, LYP-DHSD achieves multi-section yielding and exhibits excellent load-bearing capacity, deformation ability, and stable energy dissipation performance, with fatigue performance meeting code requirements. Adjusting the inner diameter significantly influences the structure’s load-bearing capacity, stiffness, and energy dissipation. Increasing the length of the constant cross-section straight segment reduces the load-bearing capacity, stiffness, and energy dissipation of LYP-DHSD. Additionally, increasing the inner and outer diameters improves material utilization efficiency initially, but it subsequently decreases. Modifying the length of the constant cross-section straight segment allows for adjustments in the plasticity distribution region of LYP-DHSD. Based on the analysis results, it is recommended that the ratio of the inner diameter to the outer diameter of LYP-DHSD be set between 0.375 and 0.625, and the ratio of the inner diameter to the length of the constant cross-section straight segment be set between 1 and 2.