TbMnO3 thin films with different crystallographic orientations were deposited epitaxially on LaAlO3 [100] and SrTiO3 [100] single crystal substrates by using pulsed laser deposition. Magnetization measurements were performed along the [110], [_110], and [001] directions of the films. Obvious magnetic anisotropy and low temperature ferromagnetism were found. Transitions at T_10, 32, 120, and 125K along different directions are observed. The susceptibility anomalies, remarkably anisotropic, are discussed on the frame of the domain wall and strain-induced distortion. Particularly, the lattice mismatch and the anisotropic thermal expansion between the films and substrates are likely responsible for the distortion behaviors.