Development of efficient, low‐cost, robust, and structure tunability electrocatalysts for hydrogen evolution reaction (HER) is one of the main subjects of present study in renewable energies. In this work, two new cuprous iodide coordination polymers (Cu‐CPs) containing bisbenzimidazole‐derived ligand, namely, {[Cu2(L1)(μ2‐I)2]·DMF}n (1) and {[Cu(L2)0.5(μ2‐I)]·DMF} (2) (L1 = (2,2′‐(1,3‐propanediyl)‐6,6′‐bis(3‐methylpyridine)bis‐1,3‐benzimidazole); L2 = (2,2′‐(1,4‐butanediyl)‐7,7′‐bis(3‐methylpyridine)bis‐1,3‐benzimidazole); DMF = dimethyl formamide), were prepared under solvothermal conditions and structurally characterized. Single‐crystal structural analysis showed that although two Cu‐CPs have a one‐dimensional (1D) chain backbone structure, the coordination environment of cuprous is different. It is found that different coordination modes of ligands L1 and L2 lead to different coordination environments of central ions in two cuprous CPs. Electrocatalytic HER of modified electrodes (CP‐1~2/glassy carbon electrode [GCE]) prepared by coating the mixed solution of acetylene black, CPs 1–2, and Nafion on the surface of GCE was investigated in 0.5 M H2SO4 electrolyte. The HER measurements show that the overpotential η10293K of CP‐1~2/GCE positively shifted 113 and 74 mV compared with bare GCE (blank electrode, −930 mV), and the Tafel slope of bare/GCE and CP‐1~2/GCE were 298, 101, and 138 mV dec−1, respectively. The results indicate that CP‐1~2/GCE could effectively catalyze and accelerate the HER behavior, with electrocatalytic activity order being CP‐1/GCE > CP‐2/GCE > bare/GCE. The higher HER activity of the CP‐1/GCE can be attributed to that the coordination deformability of cuprous ion in CP 1 is greater. Furthermore, the recognition performance of CP‐1~2/GCE for glucose was further studied by chronoamperometry in 0.1 M NaOH. The two sensors can detect glucose in a linear range from 1 μM to 4 mM with sensitivities of 13.736 and 18.945 μA mM−1, and also revealed long‐term stability and good selectivity. These results indicate that cuprous CPs deserve further investigation as potential electrocatalyst candidates.