  The excess of top quark forward-backward asymmetry ($A^t_{FB}$) reported by
the Tevatron and the enhancement of the Higgs decay to diphoton observed by the
LHC may point to a same origin of new physics. In this note we examined such
anomalies in the two-Higgs-doublet model with a color-triplet scalar. We found
that under current experimental constraints this model can simultaneously
explain both anomalies at $1\sigma$ level. Also, we examined the Higgs decay
$h\to Z\gamma$ and displayed its correlation with $h\to \gamma\gamma$. We found
that unlike other models, this model predicts a special correlation between
$h\to Z\gamma$ and $h\to \gamma\gamma$, i.e., the $Z\gamma$ rate is highly
suppressed while the $\gamma\gamma$ rate is enhanced. This behavior may help to
distinguish this model in the future high luminosity run of the LHC.
