Perovskite LaTiO3 bulk is a typical Mott-insulator with G-type antiferromagnetic order.In this work, the biaxial strain effect on the ground magnetic order of LaTiO3 films grown on various substratcs have been studied.For the compressive strain, LaTiO3 films grown on LaAlO3, LaGdO3 and SrTiO3 substrates undergo a phase transition from the original G-type antiferromagnet to A-type antiferromagnet.The underlying physical mechanisms are the strain turmed lattice distortions.While for the tensile strain, the BaTiO3 and LaScO3 substrates have been tested, which shows a tendency to transit the LaTiO3 to the C-type antiferromagnet.Furthermore, our calculations fiind that the magnetic transitions under epitaxial strains do not change the insulating fact of LaTiO3.