Beryllium carbide is used in inertial confinement fusion (ICF) capsule ablation material due to its low atomic number, low opacity, and high melting point properties. We used the method of climbing image nudged elastic band (CINEB) to calculate the diffusion barrier of copper atom in the crystal of beryllium and beryllium carbide. The diffusion barrier of copper atom in crystal beryllium is only 0.79 eV, and the barrier in beryllium carbide is larger than 2.85 eV. The three structures of beryllium carbide: anti-fluorite Be2C, Be2C-I, and Be2C-III have a good blocking effect to the diffusion of copper atom. Among them, the Be2C-III structure has the highest diffusion barrier of 6.09 eV. Our research can provide useful help for studying Cu diffusion barrier materials.