First principles electronic structure calculations have been performed for the double perovskite Bi(2)CoMnO(6) in its non-centrosymmetric polar state using the generalized gradient approximation plus the Hubbard U approach. We find that the ferromagnetic state is more favored compared to the ferrimagnetic state with both Co and Mn in high spin states. The calculated dynamical charge tensors are anisotropic reflecting a low-symmetry structure of the compound. The magnetic structure dependent phonon frequencies indicate the presence of a weak spin-phonon coupling. Using the Berry phase method, we obtain a spontaneous ferroelectric polarization of 5.88 μC cm(-2), which is close to the experimental value observed for a similar compound, Bi(2)NiMnO(6).