Motivated by a possible anomaly in the forward-backward (FB) asymmetry of top quark (A(FB)) observed at the Tevatron, we perform a model independent analysis on q (q) over bar -> t (t) over bar using an effective Lagrangian with dim-6 four-quark operators. We derive necessary conditions on new physics structures and the couplings that are consistent with the t (t) over bar production cross section and AFB measured at the Tevatron, and discuss possible new physics scenarios that could generate such dim-6 operators. (C) 2010 Elsevier B.V. All rights reserved.