The electronic properties of multiferroic BaCoF4 with ferroelectric antiferromagnetic phase and paraelectric phase are calculated using density functional theory with spin-polarized generalized-gradient approximation and plane wave pseudopotentials. It is found that anti-ferromagneticism probably favors to the ferroelectric stability at low temperature and the ion bond interaction is the main interation in the BaCoF4 system due to the strong electronegativity of F atoms. As to the CoF6 octahedron, there is entirely ionic bond between Co ion and F（2） or F（3） ions （bc plane）, but weak covalent bond between Co ion and F（1） ion and still weaker for F（4） ion. The ferroelectric distortion is only induced by relative displacement of Ba ion and F ion along c axis, and F（4） displacement contributes least to ferroelectric phase transformation . In addition, the energy of s and p orbitals of F（2） or F（3） ion is lower in the ferroelectric phase than in the centor-symmetric phase and the covalence character of F（1） ion, whose contribution to the displacement is the largest, is almost lost, which stabilizes the structure of the ferroelectric system.