We have simulated BiCoO3 films epitaxially grown along (001) direction with density functional theory computations. Leading candidates for the lowest-energy phases have been identified. The tensile strains induce magnetic phase transition in the ground state (P4mm symmetry) from a C-type antiferromagnetic order to a G-type order for the in-plane lattice parameter above 3.922 Å. The G-type antiferromagnetic order will be maintained with larger tensile strains; however, a continuous structural phase transition will occur, combining the ferroelectric and antiferrodistortive modes. In particular, the larger tensile strain allows an isostructural transition, the so-called Cowley’s ‘‘Type Zero’’ phase transitions, from Cc-(I) to Cc-(II), with a slight volume collapse. The orientation of ferroelectric polarization changes from the out-of-plane direction in the P4mm to the in-plane direction in the Pmc21 state under epitaxial tensile strain; meanwhile, the magnetic ordering temperature TN can be strikingly affected by the variation of misfit strain.