Yttrium iron garnet (YIG) film is a kind of magnetic film and has been investigated extensively because of its excellent magnetic properties and various applications in different fields. Generally, the easy-axis of the film is in-plane and can be changed from in-plane to out-of-plane by introducing some Bi3+ ions into the dodecahedral sites as it has big uniaxial anisotropy, which will be very important in magnetic bubble memories, magneto-optical devices and the new development of spin-wave logic devices. In comparison with many other preparation techniques, the liquid phase epitaxy (LPE) has been consider as a potential method of realizing perpendicular magnetization film due to its big growth-induced anisotropy. However, the LPE technique has more stringent requirements for lattice match between garnet film and gadolinium gallium garnet (GGG) substrate, especially in the growth of thick film. The lattice match is the key factor in LPE growth if the aim of experiment is to achieve a perfect quality and thick film. In most of experiments, there always exists the lattice mismatch between the film and substrate. Owing to the film and substrate have different chemical compositions, their lattice mismatch stress is unavoidable. The purpose of this paper is to investigate the effect of the stress on the anisotropy and then the magnetic domain of (BiTm)3(GaFe)5O12 single crystal film. In our experiment, the monocrystalline (BiTm)3(GaFe)5O12 films are prepared on (111)-oriented GGG substrates by LPE technique and the effect of lattice mismatch stress on the uniaxial anisotropy and magnetic domain are investigated. It is found that the lattice constant of the film is mainly determined by the content of Bi3+ in the film composition. and the increase of Bi3+ content leads to the increase of the film lattice constant, which affects the lattice mismatch stress between film and substrate. The lattice mismatch stress can adjust the perpendicular anisotropy of film which is the main reason for the domain changes. As the mismatch stress changes from tensile stress to compressive stress gradually, the magnetic bubble domain is transformed first into maze domain, and then into the partially striped domain, finally into the completely striped domain. The mismatch tensile stress is an effective method to enhance perpendicular anisotropy, when the growth-induced perpendicular anisotropy is not large enough. The bubble domain can only appear on the film with large tensile stress. The domain size is closely related to the stress. The domain width becomes wider as the mismatch stress becomes larger and it has the smallest domain size as the stress is minimum. These experimental results are very useful in controlling the uniaxial anisotropy and magnetic domain based on the change of the lattice mismatch stress in the growth process.