If the flavor dependent non-standard interactions (NSI) in neutrino propagation exist, then the matter effect is modified and the modification is parametrized by the dimensionless parameter $epsilon_{alphabeta}~(alpha,beta=e, mu, tau)$. In this paper we discuss the sensitivity of the T2HKK experiment, whose possibility is now seriously discussed as a future extension of the T2K experiment, to such NSI. On the assumption that $epsilon_{alphamu}=0~(alpha=e, mutau)$ and $epsilon_{tautau}=|epsilon_{etau}|/(1+epsilon_{ee})$, which are satisfied by other experiments to a good approximation, we find that, among the possible off-axis flux configurations of $1.3^circ$, $1.5^circ$, $2.0^circ$ and $2.5^circ$, the case of the off-axis angle $1.3^circ$ gives the highest sensitivity to $epsilon_{ee}$ and $|epsilon_{etau}|$. Our results show that the $1.3^circ$ off-axis configuration can exclude NSI for $|epsilon_{ee}|gtrsim 1$ or $|epsilon_{etau}|gtrsim 0.2$ at 3$sigma$. We also find that in the presence of NSI, T2HKK (for the off-axis angle $1.3^circ$) has better sensitivity to the two CP phases ($delta_{CP}$ and arg($epsilon_{e tau}$)) than DUNE. This is because of the synergy between the two detectors i.e., one at Kamioka and one at Korea. T2HKK has better sensitivity to the CP phases than the atmospheric neutrino experiment at Hyperkamiokande in inverted hierarchy, but in normal hierarchy the atmospheric neutrino experiment has the best sensitivity to the CP phases.
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