Monocrystalline SrMnBi₂ thin films were grown by molecular beam epitaxy (MBE), and their transport properties were investigated. A high and unsaturated linear magnetoresistance (MR) was observed, which exhibited a transition from a semi-classical weak-field B² dependence to a high-field linear dependence. An unusual nonlinear Hall resistance was also observed because of the anisotropic Dirac fermions. The two-carrier model was adopted to analyze the unusual Hall resistance quantitatively. The fitting results yielded carrier densities and mobilities of 3.75×10¹⁴ cm⁻² and 850 cm²·V⁻¹s⁻¹, respectively, for holes, and 1.468×10¹³ cm⁻², 4118 cm²·V⁻¹·s⁻¹, respectively, for electrons, with a hole-dominant conduction at 2.5 K. Hence, an effective mobility can be achieved, which is in reasonable agreement with the effective hole mobility of 1800 cm²·V⁻¹·s⁻¹, extracted from the MR. Further, the angle-dependent MR, proportional to cosθ, where θ is the angle between the external magnetic field and the perpendicular orientation of the sample plane, also implies a high anisotropy of the Fermi surface. Our results about SrMnBi₂ thin films, as one of a new class of AEMnBi₂ and AEMnSb₂ (AE= Ca, Sr, Ba, Yb, Eu) materials, suggest that they have a lot of exotic transport properties to be investigated, and that their high mobility might facilitate electronic device applications.