Motivated by a possible anomaly in the forward-backward (FB) asymmetry of top quark AFB observed at the Tevatron, we perform a model independent analysis on q \bar{q} \to t \bar{t} 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\bar{t} production cross section and AFB measured at the Tevatron, and discuss possible new physics scenarios that could generate such dim-6 operators