Electronic and magnetic properties of BiCoO(3) have been investigated using the ab initio density-functional calculations with local spin density approximation (LSDA) and LSDA+U methods. The structural stability and the origin of the multiferroism for ferroelectronic and ferromagnetic existence were addressed. It was shown that the stability of the C-type antiferromagnetic (C-AFM) structure is better than that of other possible configurations. The hybridization between Bi-O and Co-O with interplay and a local magnetic moment on the Co(3+) play important roles for the nature of the ferroelectricity and ferromagnetism. Theoretical calculations predict the insulating ground state with a band gap of 2.11 eV in the C-AFM ordering for BiCoO(3) originated from the antiferromagnetic interaction in the ab plane, which is in well agreement with experiments.