This paper obtains the energy-spectrum and eigenstate corrections of two-mode Bose-Einstein condensates (BECs) coupled by quantum tunnelling by perturbation method in both strong and weak tunnelling regions.The population imbalance between two BECs are then studied in terms of the low-lying eigenstates which also characterize the intrinsic entanglement between the two-mode BECs.The strong parity effect in the weak tunnelling region is also investigated.