Monte Carlo (MC) simulations based on lattice model were performed to study the phase diagram (anisotropy, uniaxiality and biaxiality) of liquid crystals formed by bent-cored molecules with a strong transverse dipole moment deviating from their angular bisector. It is shown that the asymmetric strong dipolar interaction enhances biaxiality slightly but encourages uniaxiality greatly and as a result suppresses the system's isotropic order, which is different from a system free from external field in that dipole moment increases biaxiality by suppressing the uniaxial and the isotropic orders simultaneously. It is also found that an external electric field encourages the biaxiality slightly but considerably enhances the uniaxiality of bent-cored liquid crystal. (C) 2016 Elsevier B.V. All rights reserved.