Heavy flavor production at the Tevatron

Using a subset of the current Run II data, the CDF and D0 have performed several measurements on heavy flavor production. In this paper, we present a new measurement of prompt charm meson production by CDF. We also report the latest CDF II measurements of inclusive J/{Psi} production and b-production without requirement of minimum transverse momentum on J/{Psi} and b-quark. They are the first measurements of the total inclusive J/{Psi} and b quark cross section in the central rapidity region at a hadron collider. The results of J/{Psi} cross section as a function of rapidity, and b-jet production cross section measured by D0 are also reviewed