The hydrogen storage and sensor properties of Cu-modified boron nitride nanocone (BNNC) structure were comprehensively investigated using the density functional theory method (DFT). By replacing nitrogen atoms with copper atoms on the BNNC structure, the hydrogen molecule's adsorption enthalpy and Gibbs free energy values were calculated as −48.6 and −16.9 kJ/mol, respectively. 4 Cu-doped BNNC structure achieved a notable hydrogen storage capacity of 5.38 wt%. The molecular dynamics calculations demonstrate that the structure modified with four Cu atoms maintains its dynamic stability. Furthermore, this study reveals that the desorption temperatures tend to rise with an increase in the number of adsorbed hydrogen molecules, and the average desorption temperature under 1 atm pressure is determined to be 332 K. The changes of work function values after hydrogen adsorption point out that the Cu-modified BNNC has Φ-sensor feature. Overall, Cu-modified BNNC structures show promising potential as hydrogen storage materials in ambient conditions.