  Top partners are well motivated in many new physics models. Usually, vector
like quarks $T_{L,R}$ are introduced to avoid the quantum anomaly. It is
crucial to probe their interactions with the standard model particles. However,
flavor changing neutral couplings are always difficult to detect directly in
the current and future experiments. In this paper, we will show how to
constrain the flavor changing neutral Yukawa coupling $Tth$ through the
di-Higgs production indirectly. We consider the simplified model including a
pair of gauge singlet $T_{L,R}$. Under the perturbative unitarity and
experimental constraints, we choose $m_T=400~\mathrm{GeV},s_L=0.2$ and
$m_T=800~\mathrm{GeV},s_L=0.1$ as benchmark points. After the analysis of
amplitude and evaluation of the numerical cross sections, we find that the
present constraints from di-Higgs production have already surpassed the
unitarity bound because of the $(y_{L,R}^{tT})^4$ behavior. For the case of
$m_T=400~\mathrm{GeV}$ and $s_L=0.2$, $\mathrm{Re}y_{L,R}^{tT}$ and
$\mathrm{Im}y_{L,R}^{tT}$ can be bounded optimally in the range $(-0.4, 0.4)$
at HL-LHC with $2\sigma$ CL. For the case of $m_T=800~\mathrm{GeV}$ and
$s_L=0.1$, $\mathrm{Re}y_{L,R}^{tT}$ and $\mathrm{Im}y_{L,R}^{tT}$ can be
bounded optimally in the range $(-0.5, 0.5)$ at HL-LHC with $2\sigma$ CL. The
anomalous triple Higgs coupling $\delta_{hhh}$ can also affect the constraints
on $y_{L,R}^{tT}$. Finally, we find that the top quark electric dipole moment
can give stronger bounds of $y_{L,R}^{tT}$ in the off-axis regions for some
scenarios.
