The epitaxial strain effects on the magnetic ground state of YTiO$_3$ films grown on LaAlO$_3$ substrates have been studied using the first-principles density-functional theory. With the in-plane compressive strain induced by LaAlO$_3$ (001) substrate, A-type antiferromagnetic order emerges against the original ferromagnetic order. This phase transition from ferromagnet to A-type antiferromagnet in YTiO$_3$ film is robust since the energy gain is about 7.64 meV per formula unit despite the Hubbard interaction and modest lattice changes, even though the A-type antiferromagnetic order does not exist in any $R$TiO$_3$ bulks. ; Comment: 3 pages, 2 figures. Proceeding of the 12th Joint MMM/Intermag Conference. Accepted by JAP