The top quark forward-backward asymmetry AtFB measured at the Tevatron is above the standard model prediction by more than 2σ deviation, which might be a harbinger for new physics. In this work we examine the contribution to AtFB in two different new physics models: one is the minimal supersymmetric model without R parity which contributes to AtFB via sparticle-mediated t channel process d¯d→t¯t; the other is the third-generation enhanced left-right model which contributes to AtFB via Z′-mediated t channel or s channel processes. We find that in the parameter space allowed by the t¯t production rate and the t¯t invariant mass distribution at the Tevatron, the left-right model can enhance AtFB to within the 2σ region of the Tevatron data for the major part of the parameter space, and in optimal case AtFB can reach 12% which is slightly below the 1σ lower bound. For the minimal supersymmetric model without R parity, only in a narrow part of the parameter space can the λ'' couplings enhance AtFB to within the 2σ region while the λ′ couplings just produce negative contributions to worsen the fit.