  The large value of non-minimal coupling constant $\xi$ required to satisfy
CMB observations in Higgs inflation violates unitarity. In this work we study
Higgs-inflation with non-canonical kinetic term of DBI form to find whether
$\xi$ can be reduced. To study the inflationary dynamics, we transform the
action to the Einstein frame, in which the Higgs is minimally coupled to
gravity with a non-canonical kinetic term and modified potential. We choose the
Higgs self coupling constant $\lambda=0.14$ for our analysis. We find that the
value of $\xi$ can be reduced from $10^{3}-10^{4}$ to $\mathcal{O}(10)$ to
satisfy Planck constraints on amplitude of scalar power spectrum. However, this
model produces a larger tensor-to-scalar ratio $r$, in comparison to the Higgs
inflation with canonical kinetic term. We also find that, to satisfy joint
constraints on scalar spectral index $n_s$ and tensor-to-scalar ratio $r$ from
Planck-2018 and bounds on $r$ from Planck and BICEP3, the value of $\xi$ should
be of the order of $10^4$. Thus, the issue of unitarity violation remains even
after considering Higgs inflation with non-canonical kinetic term
