TbMnO3 exists in an orthorhombic phase in nature. Recently, we successfully grew TbMnO3 thin films in the hexagonal phase using epitaxial stabilization techniques. In this article, we will show the details of the deposition conditions that allow us to fabricate the hexagonal TbMnO3 films on Pt–Al2O3(0001) substrates. The artificial hexagonal phase can be easily formed above 850 °C, irrespective of the oxygen partial pressure. The hexagonal TbMnO3 films showed ferroelectric properties, which are significantly enhanced compared to those of the orthorhombic TbMnO3 bulk phase. We find interesting anomalies in the magnetic and magnetodielectric properties of the TbMnO3 films at around 45 K, which should be related with the Mn3+ spin reorientation. We also find spin-glass-like behaviors in the magnetic susceptibility, which could be attributed to the geometric frustration of antiferromagnetically coupled Mn spins with an edge-sharing triangular lattice. This work shows details of the growth and properties of hexagonal TbMnO3 films.