We report the observation of highly anisotropic Dirac fermions in a Bi square net of SrMnBi(2), based on a first-principles calculation, angle-resolved photoemission spectroscopy, and quantum oscillations for high-quality single crystals. We found that the Dirac dispersion is generally induced in the (SrBi)(+) layer containing a double-sized Bi square net. In contrast to the commonly observed isotropic Dirac cone, the Dirac cone in SrMnBi(2) is highly anisotropic with a large momentum-dependent disparity of Fermi velocities of ~8. These findings demonstrate that a Bi square net, a common building block of various layered pnictides, provides a new platform that hosts highly anisotropic Dirac fermions.