We report two-dimensional quantum transport in SrMnBi${}_{2}$ single crystals. The linear energy dispersion leads to unusual nonsaturated linear magnetoresistance since all Dirac fermions occupy the lowest Landau level in the quantum limit. The transverse magnetoresistance exhibits a crossover at a critical field ${B}^{*}$ from semiclassical weak-field ${B}^{2}$ dependence to the high-field linear-field dependence. With an increase in temperature, the critical field ${B}^{*}$ increases and the temperature dependence of ${B}^{*}$ satisfies the quadratic behavior which is attributed to the Landau-level splitting of the linear energy dispersion. The effective magnetoresistant mobility ${\ensuremath{\mu}}_{\text{MR}}\ensuremath{\sim}3400$ cm${}^{2}$/V s is derived. Angular-dependent magnetoresistance and quantum oscillations suggest dominant two-dimensional (2D) Fermi surfaces. Our results illustrate the dominant 2D Dirac fermion states in SrMnBi${}_{2}$ and imply that bulk crystals with Bi square nets can be used to study low-dimensional electronic transport commonly found in 2D materials such as graphene.