  We report two dimensional Dirac fermions and quantum magnetoresistance in
single crystals of CaMnBi$_2$. The non-zero Berry's phase, small cyclotron
resonant mass and first-principle band structure suggest the existence of the
Dirac fermions in the Bi square nets. The in-plane transverse magnetoresistance
exhibits a crossover at a critical field $B^*$ from semiclassical weak-field
$B^2$ dependence to the high-field unsaturated linear magnetoresistance ($\sim
120%$ in 9 T at 2 K) due to the quantum limit of the Dirac fermions. The
temperature dependence of $B^*$ satisfies quadratic behavior, which is
attributed to the splitting of linear energy dispersion in high field. Our
results demonstrate the existence of two dimensional Dirac fermions in
CaMnBi$_2$ with Bi square nets.
