Spinel ferrites, such as CoFe2O4, can be used in various fields such as computer technology, aerospace, and medical biotechnology due to their good electromagnetic properties. Although, CoFe2O4 thin films have good application prospects in the magnetoelectric composites, the effects of strain on the electronic structure and magnetic properties of cobalt ferrite film have not been reported. Through the use of two-dimensional strain model closer to the epitaxial growth experiments, the films of Cobalt ferrite are simulated on various substrates with a realistic biaxial strain model by first-principles plane-wave pseudopotential method based on density functional theory, and combined with the generalized gradient approximation in the paper. And the structural stabilities, electronic structures and magnetic properties of CoFe2O4 films are studied. The results show that the inverse spinel is still energetically favored under strain, but the energy difference decreases, thus Fe3+ions in the tetrahedral sites and Co2+ ions in the octahedral sites are easier to exchange their positions. As the strain increases, the band gap of cobalt ferrite becomes narrower, and the magnetic moment of atom in the lattice changes, while the net magnetic moment changes little.