  A hint of a new resonance at a mass of 750\,GeV has been observed in the
diphoton channel of LHC Run 2 at $\sqrt{s}=13$ TeV. The signal rate is too
large to interpret it as a new Higgs boson in the context of weakly-coupled
renormalizable models. One way is to reduce its total decay rate, which is
possible if the CP-even heavy Higgs boson $H^0$ in the aligned two Higgs
doublet model becomes top-phobic. To ensure sufficient gluon fusion production,
we introduce vector-like quarks (VLQ). The Higgs precision data as well as the
exclusion limits from no excesses in other 8 TeV LHC searches of $Z\gamma$,
$b\bar{b}$, $\tau^+\tau^-$, and $jj$ channels are simultaneously included. In
Type I, top-phobic $H^0$ cannot explain the 750\,GeV diphoton signal and the
Higgs precision data simultaneously since the universal Yukawa couplings of the
up-type and down-type VLQs always make more contribution to $h^0$ than to
$H^0$. In Type II, small Yukawa coupling of the up-type VLQ but sizable Yukawa
coupling for the down-type VLQ is shown to explain the signal while satisfying
other LHC exclusion limits.
