An electrochemical enzyme-free glucose sensor based on a novel material with high catalytic performance was constructed. Specifically, a covalent-organic framework (COFBD) with abundant O,N,O′-metal chelating sites was firstly grown on the surface of SiO2 sacrificial template and then coordinated with Ni2+. Finally, Ni/NiO/cellular carbon foam (Ni/NiO/NC) nanocomposite was obtained by carbonizing the above material and removing the SiO2 template through NaOH etching. The electrocatalytic performance of Ni/NiO/NC could be adjusted by cavity size of NC and size of Ni/NiO nanoparticles. The enzyme-free glucose sensor based on Ni/NiO/NC showed a low detection limit of 0.2 μM, a wide detection range of 0.6 μM–8.6 mM and a high sensitivity of 76.03 μA mM−1 cm−2. Moreover, the paper-based wearable glucose sensor was also implemented and the results exhibited that the detection limit was 0.4 μM, the linear range was 1.1 μM–5.2 mM and the sensitivity was 42.38 μA mM−1 cm−2. The electrochemical enzyme-free glucose sensor also showed outstanding practical application performance for detection of glucose in real samples of juice, human serum and sweat. The works provided a method to construct novel material with good catalytic performance for sensitive glucose sensor.