The realization of ferromagnetism or ferrimagnetism in BiCrO3 is crucial for its potential application in magnetoelectronic devices. It is known from experiment that the antiferromagnetic monoclinic phase of BiCrO3 transits to orthorhombic as pressure beyond 1GPa. Here, we present a first-principles study of the magnetism of orthorhombic BiCrO3 under pressures up to 80GPa. We find that the energy difference between its ferromagnetic phase and the ground state of G-type anti-ferromagnetic phase becomes greater as the pressure increases, as well as the estimated magnetic transition temperature TN. This implies the difficulty of transforming BiCrO3 into ferromagnetism by external pressure, and thus other approaches (such as doping magnetic ions) are necessary to explore its potential application in magnetoelectronic devices.