Atomistic simulations are carried out on a serials of symmetric and asymmetric Σ3 [1 10] and Σ5 [0 0 1] grain boundaries (GBs) of Cu to investigate their structures and mechanical response under tension. The equilibrium OK GB structures are generated by molecular statics simulation. It is found that Σ3 and Σ5 asymmetric GBs with different inclination angles are composed of only two structural units which are corresponding to their symmetric GBs. Molecular dynamics simulations are performed by applying a constant tensile strain on the bicrystal model with different Σ3 and Σ5 GBs. Simulation results show that the maximum tensile strength of the symmetric Σ3 and Σ5 GBs are higher than their asymmetric GBs, suggesting the symmetric GBs may have a more stable boundary structures.