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