The stable chemical potential phases of BiXO3 (X= Cr, Mn, Fe, Ni) are studied by density functional theory with the consideration of thermodynamics equilibrium conditions. It is found that the BiFeO3 and BiCrO3 have stable chemical potential regions and are expected to be synthesized, under thermodynamic equilibrium conditions. On the contrary, no stable regions are found for BiMnO3 and BiNiO3, indicating that they are hard to synthesize. Therefore the approaches to their preparation under non-thermodynamic equilibrium conditions should be considered.