  The Einstein-dilaton-Gauss-Bonnet (EdGB) theory is a modified theory which
include a scalar field to couple with the higher order curvature terms. It has
already been constrained with various observations include the gravitational
wave (GW) with LIGO, Virgo and KAGRA (LVK) Collaboration. In this work, we
study the problem of using the GW of Extreme Mass-Ratio Inspiral (EMRI) to
constrain the EdGB theory. We use the "numerical kludge (NK)" method to
construct the waveform of EMRI in the EdGB theory, focusing on the case when
the central black hole is spinless. We then study how a future space-borne
gravitational wave detector, TianQin, for example, can place constraints on the
EdGB theory through the detection of EMRIs. With the analysis using mismatch
and Fisher Information Matrix (FM), we find that the EdGB parameter
$\sqrt{\alpha}$ is expected to be constrained to the level of
$\sim\mathcal{O}(0.1)$ km.
