Perovskite LaTiO$_3$ bulk is a typical Mott-insulator with G-type antiferromagnetic order. In this work, the biaxial strain effects on the ground magnetic order of LaTiO$_3$ films grown on various substrates have been studied. For the compressive strain, LaTiO$_3$ films grown on LaAlO$_3$, LaGaO$_3$, and SrTiO$_3$ substrates undergo a phase transition from the original G-type antiferromagnet to A-type antiferromagnet. The underlying physical mechanisms are the lattice distortions tunned by strain. While for the tensile strain, the BaTiO$_3$ and LaScO$_3$ substrates have been tested, which show a tendency to transit the LaTiO$_3$ to the C-type antiferromagnet. Furthermore, our calculations find that the magnetic transitions under epitaxial strain do not change the insulating fact of LaTiO$_3$. ; Comment: 3 pages, 3 figures. Proceeding of the 58th MMM conference, accepted